diff --git a/README.md b/README.md
index 868120f..504bd81 100644
--- a/README.md
+++ b/README.md
@@ -1025,6 +1025,8 @@ removing the address only stops the wallet tracking it. It explains the way
 back: delete the whole wallet in Settings and import its backup again. The scan
 after an import finds only addresses with on-chain activity. When the address
 holds anything, the screen lists the holdings and the USD total under a warning.
+An ETH balance that no refresh has read counts as holding something. The warning
+then reads "This address may hold a balance."
 
 "Remove Address" removes the address and its site permissions. It returns to
 Home with the flash message "Address removed." The wallet's `nextIndex` is not
@@ -1212,13 +1214,25 @@ there in place of a zero. It does so after each of these:
 - an address or a wallet is added;
 - the network is switched.
 
-This lasts until a refresh has read the token's balance at every address.
+This lasts until a refresh in the popup has read the token's balance at every
+address.
+
+An address's ETH balance is `null` until a refresh has read that address. This
+holds for a new address, and for every address after a network switch. While it
+is `null`:
+
+- the balance lists show "quantity unknown";
+- Home's ETH balance reads `unknown (ETH)`;
+- Send reads `Current balance: unknown (ETH)`, and "Max" fills in nothing;
+- "Send" is not refused for a zero balance;
+- the address has no total;
+- DeleteAddress shows its warning.
 
 Only a whole number from 0 to 80 counts as a token's decimals. A token's
-`decimals` is stored only as a source reported it, never guessed. A `null`
-balance means the decimals are unknown, never that the balance is zero. While
-"Use Blockscout" is off, the bundled list and the tracked tokens may lack a
-token's symbol or decimals. The approval and status screens then add a line
+`decimals` is stored only as a source reported it, never guessed. A token's
+`null` balance means the decimals are unknown, never that the balance is zero.
+While "Use Blockscout" is off, the bundled list and the tracked tokens may lack
+a token's symbol or decimals. The approval and status screens then add a line
 under that token saying that Blockscout's report is not used.
 
 The wallet's own ERC-20 send is encoded with the decimals the screen showed. At
@@ -1254,6 +1268,7 @@ unpriced holding was left out. `formatAddressTotal()` renders that result the
 same way on every screen:
 
 - on Sepolia, or before the first price fetch: no total;
+- while the address's ETH balance is unknown: no total;
 - everything priced: `Total: $5,500.00`;
 - part priced: `Total: $3,000.00 plus unpriced tokens`;
 - nothing priced but something held: `Total: unpriced tokens only`.
diff --git a/src/popup/index.js b/src/popup/index.js
index 90cf94e..f9c8dd9 100644
--- a/src/popup/index.js
+++ b/src/popup/index.js
@@ -99,12 +99,12 @@ let refreshTimer = null;
 //
 // The save also deletes `balanceNotFetched` from each tracked token whose
 // balance this refresh read at every address. A refresh that did not read every
-// address this page now holds deletes no `balanceNotFetched`. Adding a token
-// sets that field (trackToken() in src/popup/views/helpers.js). So does adding
-// an address, and so does a network switch. The save takes the field off the
-// matching tokens of the stored record (clearBalanceNotFetched() in
-// src/shared/state.js). The rest of the stored tracked token list stays as it
-// is.
+// address this page now holds, and every address in the stored record, deletes
+// no `balanceNotFetched`. Adding a token sets that field (trackToken() in
+// src/popup/views/helpers.js). So does adding an address, and so does a network
+// switch. The save takes the field off the matching tokens of the stored record
+// (clearBalanceNotFetched() in src/shared/state.js). The rest of the stored
+// tracked token list stays as it is.
 //
 // Once the save is done, the wallet list is drawn again. So are the balances
 // on AddressDetail or AddressToken when that screen is up. No other screen is
@@ -151,7 +151,10 @@ async function doRefreshAndRender() {
             if (!stored.useBlockscout) {
                 dropUntrackedTokens(state.wallets, stored.trackedTokens);
             }
-            const readEveryAddress = state.wallets.every((wallet) =>
+            const readEveryAddress = [
+                ...state.wallets,
+                ...stored.wallets,
+            ].every((wallet) =>
                 wallet.addresses.every((addr) => refreshed.has(addr.address)),
             );
             if (readEveryAddress) clearBalanceNotFetched(stored, readTokens);
diff --git a/src/popup/views/addWallet.js b/src/popup/views/addWallet.js
index abdc485..3689e21 100644
--- a/src/popup/views/addWallet.js
+++ b/src/popup/views/addWallet.js
@@ -190,7 +190,7 @@ async function importMnemonic(ctx) {
             {
                 address: firstAddress,
                 index: 0,
-                balance: "0.0000",
+                balance: null,
                 tokenBalances: [],
             },
         ],
@@ -218,7 +218,7 @@ async function importMnemonic(ctx) {
         wallet.addresses = scan.addresses.map((a) => ({
             address: a.address,
             index: a.index,
-            balance: "0.0000",
+            balance: null,
             tokenBalances: [],
         }));
         wallet.nextIndex = scan.nextIndex;
@@ -267,7 +267,7 @@ async function importPrivateKey(ctx) {
         type: "key",
         name: "Wallet " + walletNum,
         encryptedSecret: encrypted,
-        addresses: [{ address: addr, balance: "0.0000", tokenBalances: [] }],
+        addresses: [{ address: addr, balance: null, tokenBalances: [] }],
     });
     markTrackedTokensNotFetched();
     state.hasWallet = true;
@@ -328,7 +328,7 @@ async function importXprvKey(ctx) {
             {
                 address: firstAddress,
                 index: 0,
-                balance: "0.0000",
+                balance: null,
                 tokenBalances: [],
             },
         ],
@@ -356,7 +356,7 @@ async function importXprvKey(ctx) {
         wallet.addresses = scan.addresses.map((a) => ({
             address: a.address,
             index: a.index,
-            balance: "0.0000",
+            balance: null,
             tokenBalances: [],
         }));
         wallet.nextIndex = scan.nextIndex;
diff --git a/src/popup/views/addressDetail.js b/src/popup/views/addressDetail.js
index fc02656..002f623 100644
--- a/src/popup/views/addressDetail.js
+++ b/src/popup/views/addressDetail.js
@@ -273,7 +273,8 @@ function init(_ctx) {
             state.wallets[state.selectedWallet].addresses[
                 state.selectedAddress
             ];
-        if (!addr.balance || parseFloat(addr.balance) === 0) {
+        // A null balance is one no refresh has read, so it is not refused.
+        if (parseFloat(addr.balance) === 0) {
             showFlash("Cannot send \u2014 zero balance.");
             return;
         }
diff --git a/src/popup/views/addressToken.js b/src/popup/views/addressToken.js
index 1ee9a75..6754afe 100644
--- a/src/popup/views/addressToken.js
+++ b/src/popup/views/addressToken.js
@@ -161,7 +161,8 @@ function renderBalance() {
     const tokenId = state.selectedToken;
     let amount, price;
     if (tokenId === "ETH") {
-        amount = parseFloat(addr.balance || "0");
+        // null when no refresh has read the balance.
+        amount = unknownableAmount(addr.balance);
         price = getPrice("ETH");
     } else {
         const id = tokenId.toLowerCase();
@@ -372,7 +373,8 @@ function init(_ctx) {
             state.wallets[state.selectedWallet].addresses[
                 state.selectedAddress
             ];
-        if (!addr.balance || parseFloat(addr.balance) === 0) {
+        // A null balance is one no refresh has read, so it is not refused.
+        if (parseFloat(addr.balance) === 0) {
             if (state.selectedToken === "ETH") {
                 showFlash("Cannot send \u2014 zero balance.");
                 return;
diff --git a/src/popup/views/deleteAddress.js b/src/popup/views/deleteAddress.js
index f39474f..2fba841 100644
--- a/src/popup/views/deleteAddress.js
+++ b/src/popup/views/deleteAddress.js
@@ -87,15 +87,22 @@ function recoveryPathText(wallet) {
 // when every holding here is one with no price, since "$0.00" directly under
 // "This address holds a balance." is a contradiction. A token holding below
 // 0.000001 does not count, as the lines below leave it out.
+//
+// While no refresh has read the ETH balance the address may be empty, so the
+// sentence says "may hold".
 function balanceWarningHtml(addr) {
     if (!addressHoldsFunds(addr)) return " ";
     const line = formatAddressTotal(getAddressValue(addr));
     const total = line
         ? `<div class="text-xs text-muted mt-1">${escapeHtml(line)}</div>`
         : "";
+    const sentence =
+        addr.balance == null
+            ? "This address may hold a balance."
+            : "This address holds a balance.";
     return (
-        `<p class="mb-1">This address holds a balance. Removing it does not ` +
-        `move or spend anything; the balance stays at the address.</p>` +
+        `<p class="mb-1">${sentence} Removing it does not move or spend ` +
+        `anything; the balance stays at the address.</p>` +
         balanceLinesForAddress(addr, state.trackedTokens, false) +
         total
     );
diff --git a/src/popup/views/helpers.js b/src/popup/views/helpers.js
index 9198ee0..61801fb 100644
--- a/src/popup/views/helpers.js
+++ b/src/popup/views/helpers.js
@@ -283,9 +283,10 @@ function showFlash(msg, duration = 2000) {
     flashTimer = setTimeout(clearFlash, duration);
 }
 
-// A stored token balance as a number, or null when there is no number in it.
-// balances.js writes null for a holding whose scale nothing knows, and this
-// keeps that null from becoming a zero one dereference later.
+// A stored balance as a number, or null when there is no number in it.
+// balances.js writes null for a holding whose scale nothing knows, and an
+// address's ETH balance is null until a refresh has read it. This keeps that
+// null from becoming a zero one dereference later.
 function unknownableAmount(balance) {
     if (balance == null) return null;
     const n = parseFloat(balance);
@@ -394,10 +395,10 @@ function formatFee(wei, symbol, chainId) {
 // holding renders through here.
 //
 // `amount` is null for a holding whose scale nothing knows
-// (https://git.eeqj.de/sneak/AutistMask/issues/349). There is no quantity to
-// print for it and no fiat value to derive from one, and printing 0.0000 for
-// a real holding is the failure this whole rule exists to prevent, so the row
-// says so instead.
+// (https://git.eeqj.de/sneak/AutistMask/issues/349), and for a balance no
+// refresh has read. There is no quantity to print for it and no fiat value to
+// derive from one, and printing 0.0000 for a real holding is the failure this
+// whole rule exists to prevent, so the row says so instead.
 function balanceLine(symbol, amount, price, tokenId) {
     const qty = amount === null ? "quantity unknown" : amount.toFixed(4);
     const usd =
@@ -440,7 +441,7 @@ function markTrackedTokensNotFetched() {
 function balanceLinesForAddress(addr, trackedTokens, showZero) {
     let html = balanceLine(
         nativeCurrency(),
-        parseFloat(addr.balance || "0"),
+        unknownableAmount(addr.balance),
         getPrice("ETH"),
         "ETH",
     );
@@ -493,7 +494,10 @@ function balanceLinesForAddress(addr, trackedTokens, showZero) {
 // about holdings must ask this, not the rendered figure.
 function addressHoldsFunds(addr) {
     if (!addr) return false;
-    if (parseFloat(addr.balance || "0") > 0) return true;
+    // A null or absent ETH balance reads as unknown, so the address may hold
+    // funds. Warning about funds must err towards warning.
+    if (addr.balance == null) return true;
+    if (parseFloat(addr.balance) > 0) return true;
     for (const t of addr.tokenBalances || []) {
         if (isBelowOneMillionth(t.balance)) continue;
         // A null balance is a holding whose amount could not be stated —
diff --git a/src/popup/views/home.js b/src/popup/views/home.js
index 3758fbe..c6c880f 100644
--- a/src/popup/views/home.js
+++ b/src/popup/views/home.js
@@ -3,6 +3,7 @@ const {
     showView,
     showFlash,
     balanceLinesForAddress,
+    unknownableAmount,
     markTrackedTokensNotFetched,
     isoDate,
     timeAgo,
@@ -76,10 +77,16 @@ function renderTotalValue() {
         if (subEl) subEl.innerHTML = "&nbsp;";
         return;
     }
-    const ethBal = parseFloat(addr.balance || "0");
-    const ethStr = ethBal.toFixed(4) + " " + nativeCurrency();
-    const ethUsd = ethPrice ? " (" + formatUsd(ethBal * ethPrice) + ")" : "";
-    el.textContent = ethStr + ethUsd;
+    const ethBal = unknownableAmount(addr.balance);
+    if (ethBal === null) {
+        el.textContent = "unknown (" + nativeCurrency() + ")";
+    } else {
+        const ethStr = ethBal.toFixed(4) + " " + nativeCurrency();
+        const ethUsd = ethPrice
+            ? " (" + formatUsd(ethBal * ethPrice) + ")"
+            : "";
+        el.textContent = ethStr + ethUsd;
+    }
 
     if (subEl) {
         subEl.innerHTML =
@@ -411,7 +418,7 @@ function render(ctx) {
             wallet.addresses.push({
                 address: newAddr,
                 index: wallet.nextIndex,
-                balance: "0.0000",
+                balance: null,
                 tokenBalances: [],
             });
             wallet.nextIndex++;
@@ -498,7 +505,8 @@ function init(ctx) {
             return;
         }
         const addr = currentAddress();
-        if (!addr.balance || parseFloat(addr.balance) === 0) {
+        // A null balance is one no refresh has read, so it is not refused.
+        if (parseFloat(addr.balance) === 0) {
             showFlash("Cannot send \u2014 zero balance.");
             return;
         }
diff --git a/src/popup/views/send.js b/src/popup/views/send.js
index b8f3301..8895370 100644
--- a/src/popup/views/send.js
+++ b/src/popup/views/send.js
@@ -230,11 +230,14 @@ function updateSendBalance() {
     attachCopyHandlers($("send-from"));
     const token = state.selectedToken || $("send-token").value;
     if (token === "ETH") {
+        // A null balance is one no refresh has read.
         $("send-balance").textContent =
-            "Current balance: " +
-            truncateAmountNeverZero(addr.balance || "0") +
-            " " +
-            nativeCurrency();
+            addr.balance == null
+                ? "Current balance: unknown (" + nativeCurrency() + ")"
+                : "Current balance: " +
+                  truncateAmountNeverZero(addr.balance) +
+                  " " +
+                  nativeCurrency();
     } else {
         const symbol = resolveSymbol(
             token,
@@ -289,6 +292,12 @@ async function fillMaxAmount() {
         return;
     }
 
+    // A null balance is one no refresh has read.
+    if (addr.balance == null) {
+        showFlash("This token's balance is unknown.");
+        return;
+    }
+
     // The fee is estimated for this recipient, as the confirmation screen
     // estimates it: sending to a contract can cost more gas.
     const to = $("send-to").value.trim();
@@ -306,7 +315,7 @@ async function fillMaxAmount() {
             provider.estimateGas({
                 from: addr.address,
                 to,
-                value: parseEther(addr.balance || "0"),
+                value: parseEther(addr.balance),
             }),
         ]);
         feeWei = feeReserveWei(gasLimit, feeData);
@@ -321,8 +330,10 @@ async function fillMaxAmount() {
     }
     // While the estimate was in flight the user left the screen (and perhaps
     // opened it again), typed an amount, or changed the address, the holding
-    // or the recipient: what they did wins.
+    // or the recipient: what they did wins. A network switch in that time
+    // leaves no balance to fill in from.
     if (
+        addr.balance == null ||
         state.currentView !== "send" ||
         sendScreenOpenings !== opening ||
         currentAddress()?.address !== addr.address ||
diff --git a/src/shared/chainSwitch.js b/src/shared/chainSwitch.js
index 2b8a977..fe298f9 100644
--- a/src/shared/chainSwitch.js
+++ b/src/shared/chainSwitch.js
@@ -49,7 +49,7 @@ function clearPopupCaches() {
 // follow runs first, and this switch is made after it.
 //
 // The save writes only the fields that differ from what this page last saved.
-// When this page last saved a balance of "0", clearing that balance is no
+// When this page last saved a balance of null, clearing that balance is no
 // change. So the switch also resets these fields in the stored record:
 //
 // - every address's balance and token balances;
@@ -100,7 +100,7 @@ async function onChainSwitch(newNetworkId) {
         stored.fraudContracts = [];
         for (const wallet of stored.wallets) {
             for (const addr of wallet.addresses) {
-                addr.balance = "0";
+                addr.balance = null;
                 addr.tokenBalances = [];
             }
         }
diff --git a/src/shared/chainSwitchFields.js b/src/shared/chainSwitchFields.js
index 7314a71..4c33998 100644
--- a/src/shared/chainSwitchFields.js
+++ b/src/shared/chainSwitchFields.js
@@ -68,10 +68,11 @@ function applyChainSwitchFields(s, newNetworkId) {
 
     // Clear per-address balances and token balances so stale data
     // from the previous chain is never displayed while the first
-    // refresh on the new chain is in flight.
+    // refresh on the new chain is in flight. A balance of null is one no
+    // refresh has read: it reads as unknown until one has, not as 0.0000.
     for (const wallet of s.wallets || []) {
         for (const addr of wallet.addresses || []) {
-            addr.balance = "0";
+            addr.balance = null;
             addr.tokenBalances = [];
         }
     }
@@ -108,7 +109,7 @@ function copyChainSwitchFields(s, switched) {
     for (const wallet of s.wallets) {
         for (const addr of wallet.addresses) {
             const got = stored.get(addr.address);
-            addr.balance = got ? got.balance : "0";
+            addr.balance = got ? got.balance : null;
             addr.tokenBalances = got ? got.tokenBalances : [];
         }
     }
diff --git a/src/shared/prices.js b/src/shared/prices.js
index 240fb59..1c9d0d0 100644
--- a/src/shared/prices.js
+++ b/src/shared/prices.js
@@ -146,7 +146,8 @@ function formatUsd(amount) {
 // way an absent holders_count is not a count of zero.
 //
 //   usd:     the value of the holdings a price is known for, or null when
-//            nothing is knowable at all — testnet, or before the first fetch.
+//            no total can be stated — testnet, before the first fetch, or an
+//            ETH balance no refresh has read.
 //   partial: the address also holds a token with no price, so usd is a floor
 //            and not the total.
 //
@@ -155,7 +156,8 @@ function getAddressValue(addr) {
     const { currentNetwork } = require("./state");
     if (currentNetwork().isTestnet) return { usd: null, partial: false };
     if (!prices.ETH) return { usd: null, partial: false };
-    let usd = parseFloat(addr.balance || "0") * prices.ETH;
+    if (addr.balance == null) return { usd: null, partial: false };
+    let usd = parseFloat(addr.balance) * prices.ETH;
     let partial = false;
     for (const token of addr.tokenBalances || []) {
         // A holding below 0.000001 is left out, as the balance lists leave it
diff --git a/tests/addedTokenBalance.test.js b/tests/addedTokenBalance.test.js
index 1fcf2e6..84f4f79 100644
--- a/tests/addedTokenBalance.test.js
+++ b/tests/addedTokenBalance.test.js
@@ -15,6 +15,10 @@
 // added, and after a network switch, so it reads the same until a refresh has
 // read it (https://git.eeqj.de/sneak/AutistMask/issues/720).
 //
+// An address's ETH balance is null until a refresh has read that address, so
+// its ETH line reads the same, and Send states it as unknown
+// (https://git.eeqj.de/sneak/AutistMask/issues/736).
+//
 // Driven through the real popup over a stored profile on Ethereum Mainnet,
 // with "Show tracked tokens with zero balance" on, as it is by default.
 
@@ -125,10 +129,10 @@ function bootOnDerivingWallet() {
 }
 
 // Holds the next balance refresh open. The returned function lets it finish
-// with the address's ETH balance at 2 and `tokenBalances` as its token
-// entries, having read the balance of every token tracked when it started.
-// Given null, it finishes having read no token's balance, as when every
-// balanceOf fails, and leaves the token entries as they were.
+// with every address's ETH balance at 2 and `tokenBalances` as the first
+// address's token entries, having read the balance of every token tracked when
+// it started. Given null, it finishes having read no token's balance, as when
+// every balanceOf fails, and leaves the token entries as they were.
 function holdNextRefresh(page) {
     const { refreshBalances } = require("../src/shared/balances");
     let release;
@@ -138,7 +142,9 @@ function holdNextRefresh(page) {
             const tokenBalances = await new Promise((resolve) => {
                 release = resolve;
             });
-            wallets[0].addresses[0].balance = "2.0";
+            for (const wallet of wallets) {
+                for (const addr of wallet.addresses) addr.balance = "2.0";
+            }
             if (tokenBalances === null) return [];
             wallets[0].addresses[0].tokenBalances = tokenBalances;
             return read;
@@ -244,6 +250,22 @@ function newTokenRowsOnHome(page) {
         );
 }
 
+// Every ETH row in the balance list in element `id`, as markup, in the order
+// the list holds them.
+function ethRows(page, id) {
+    return page
+        .node(id)
+        .innerHTML.split("<div ")
+        .filter((row) => row.includes('data-token="ETH"'));
+}
+
+// A stored profile whose one address no refresh has read.
+function profileNotRead(extra) {
+    const profile = unversionedValidProfile(extra);
+    profile.wallets[0].addresses[0].balance = null;
+    return profile;
+}
+
 // The "+" button Home draws for the first wallet. As in firstRemoveButton(),
 // the list hands Home a stand-in for that button each time it is drawn, and
 // `press()` presses the last one drawn. Call it before Home next draws its list.
@@ -760,3 +782,277 @@ test("after a switch saved by the background, a tracked token reads quantity unk
     expect(row).toContain("quantity unknown");
     expect(row).not.toContain("0.0000");
 });
+
+test("a refresh deletes no balanceNotFetched while the stored record holds an address it did not read", async () => {
+    const page = await bootOnAddress({
+        trackedTokens: [{ ...NEW_TRACKED, balanceNotFetched: true }],
+    });
+    // Another popup page adds an address. This page is not told of the write.
+    const record = page.storage.read("autistmask");
+    record.wallets[0].addresses.push({
+        address: "0x" + "dd".repeat(20),
+        balance: null,
+        tokenBalances: [],
+    });
+    page.storage.write("autistmask", record);
+
+    await refreshOnce(page, []);
+
+    expect(
+        page.storage.read("autistmask").trackedTokens[0].balanceNotFetched,
+    ).toBe(true);
+    expect(newTokenRow(page)).toContain("quantity unknown");
+});
+
+test("an address just added reads quantity unknown for ETH until a refresh has read it, then the fetched balance", async () => {
+    const page = await bootOnDerivingWallet();
+    const plus = plusButton(page);
+    await refreshOnce(page, []);
+    const finish = holdNextRefresh(page);
+
+    await plus.press();
+    await page.settle();
+
+    const [held, added] = ethRows(page, "wallet-list");
+    expect(held).toContain("2.0000");
+    expect(added).toContain("quantity unknown");
+    expect(added).not.toContain("0.0000");
+    expect(
+        page.storage.read("autistmask").wallets[0].addresses[1].balance,
+    ).toBeNull();
+
+    await finish([]);
+
+    expect(ethRows(page, "wallet-list")[1]).toContain("2.0000");
+});
+
+test('an address "+" adds during a refresh reads quantity unknown for ETH when that refresh returns', async () => {
+    const page = await bootOnDerivingWallet();
+    const plus = plusButton(page);
+    await refreshOnce(page, []);
+    const finishRunning = holdNextRefresh(page);
+    const ticking = page.tick();
+    await page.settle();
+
+    await plus.press();
+    await page.settle();
+    const finishNext = holdNextRefresh(page);
+    await finishRunning([]);
+    await ticking;
+
+    const added = ethRows(page, "wallet-list")[1];
+    expect(added).toContain("quantity unknown");
+    expect(added).not.toContain("0.0000");
+
+    await finishNext([]);
+
+    expect(ethRows(page, "wallet-list")[1]).toContain("2.0000");
+});
+
+test.each([FROM_PHRASE, FROM_PRIVATE_KEY, FROM_XPRV])(
+    "a wallet just added from $tab reads quantity unknown for ETH until a refresh has read it",
+    async (source) => {
+        const page = await bootPopup(unversionedValidProfile());
+        const finish = holdNextRefresh(page);
+
+        await addWallet(page, source);
+
+        const added = ethRows(page, "wallet-list")[1];
+        expect(added).toContain("quantity unknown");
+        expect(added).not.toContain("0.0000");
+
+        await finish([]);
+
+        expect(ethRows(page, "wallet-list")[1]).toContain("2.0000");
+    },
+);
+
+test.each([FROM_PHRASE, FROM_XPRV])(
+    "addresses the scan finds for a wallet from $tab read quantity unknown for ETH until a refresh has read them",
+    async (source) => {
+        const page = await bootPopup(unversionedValidProfile());
+        const { scanForAddresses } = require("../src/shared/balances");
+        let finish;
+        scanForAddresses.mockImplementationOnce(async () => {
+            await refreshOnce(page, []);
+            finish = holdNextRefresh(page);
+            return {
+                addresses: [
+                    { address: "0x" + "dd".repeat(20), index: 0 },
+                    { address: "0x" + "ee".repeat(20), index: 1 },
+                ],
+                nextIndex: 2,
+            };
+        });
+
+        await addWallet(page, source);
+
+        const [, first, second] = ethRows(page, "wallet-list");
+        for (const found of [first, second]) {
+            expect(found).toContain("quantity unknown");
+            expect(found).not.toContain("0.0000");
+        }
+
+        await finish([]);
+
+        expect(ethRows(page, "wallet-list")[2]).toContain("2.0000");
+    },
+);
+
+test("after a network switch in Settings, the ETH line reads quantity unknown until a refresh has read it, then the fetched balance", async () => {
+    const page = await bootOnAddress();
+
+    await page.click("btn-settings");
+    await chooseNetwork(page, "sepolia");
+    await page.click("btn-settings-back");
+
+    expect(page.visibleViews()).toEqual(["address"]);
+    const [row] = ethRows(page, "address-balances");
+    expect(row).toContain("quantity unknown");
+    expect(row).not.toContain("0.0000");
+    expect(
+        page.storage.read("autistmask").wallets[0].addresses[0].balance,
+    ).toBeNull();
+
+    await refreshOnce(page, []);
+
+    expect(ethRows(page, "address-balances")[0]).toContain("2.0000");
+});
+
+test("after a switch saved by the background, the ETH line reads quantity unknown until a refresh has read it, then the fetched balance", async () => {
+    const page = await bootOnAddress();
+    const {
+        applyChainSwitchFields,
+    } = require("../src/shared/chainSwitchFields");
+    const record = page.storage.read("autistmask");
+    applyChainSwitchFields(record, "sepolia");
+    page.storage.write("autistmask", record);
+
+    // The popup takes the switch, and this refresh reads no ETH balance.
+    await page.tick();
+
+    const [row] = ethRows(page, "address-balances");
+    expect(row).toContain("quantity unknown");
+    expect(row).not.toContain("0.0000");
+
+    await refreshOnce(page, []);
+
+    expect(ethRows(page, "address-balances")[0]).toContain("2.0000");
+});
+
+test("a switch taken from the stored record leaves an address the record does not have with no ETH balance", () => {
+    const {
+        copyChainSwitchFields,
+    } = require("../src/shared/chainSwitchFields");
+    const taker = {
+        wallets: [
+            {
+                addresses: [
+                    { address: "0x1", balance: "1.5", tokenBalances: [] },
+                ],
+            },
+        ],
+    };
+
+    copyChainSwitchFields(taker, { wallets: [] });
+
+    expect(taker.wallets[0].addresses[0].balance).toBeNull();
+});
+
+test("closed and opened again before any refresh has read it, the ETH line still reads quantity unknown", async () => {
+    const closed = await bootOnAddress();
+    await closed.click("btn-settings");
+    await chooseNetwork(closed, "sepolia");
+    await closed.click("btn-settings-back");
+    cleanupPopup();
+
+    const page = await bootPopup(undefined, { storage: closed.storage });
+
+    expect(page.visibleViews()).toEqual(["address"]);
+    const [row] = ethRows(page, "address-balances");
+    expect(row).toContain("quantity unknown");
+    expect(row).not.toContain("0.0000");
+});
+
+test("Home's ETH balance reads unknown until a refresh has read it, then the fetched balance", async () => {
+    const page = await bootPopup(profileNotRead());
+
+    expect(page.visibleViews()).toEqual(["main"]);
+    expect(page.text("total-value")).toBe("unknown (ETH)");
+
+    await refreshOnce(page, []);
+
+    expect(page.text("total-value")).toBe("2.0000 ETH");
+});
+
+test("AddressToken for ETH reads quantity unknown until a refresh has read it, then the fetched balance", async () => {
+    const page = await bootPopup(
+        profileNotRead({
+            currentView: "address-token",
+            viewStack: ["main", "address"],
+            selectedWallet: 0,
+            selectedAddress: 0,
+            selectedToken: "ETH",
+        }),
+    );
+
+    expect(page.visibleViews()).toEqual(["address-token"]);
+    const before = page.node("address-token-balance").innerHTML;
+    expect(before).toContain("quantity unknown");
+    expect(before).not.toContain("0.0000");
+
+    await refreshOnce(page, []);
+
+    expect(page.node("address-token-balance").innerHTML).toContain("2.0000");
+});
+
+test.each([
+    ["main", {}, "btn-main-send"],
+    [
+        "address",
+        { currentView: "address", selectedWallet: 0, selectedAddress: 0 },
+        "btn-send",
+    ],
+    [
+        "address-token",
+        {
+            currentView: "address-token",
+            viewStack: ["main", "address"],
+            selectedWallet: 0,
+            selectedAddress: 0,
+            selectedToken: "ETH",
+        },
+        "btn-address-token-send",
+    ],
+])(
+    "Send from %s reads an unread ETH balance as unknown, Max says so, and only a balance read as zero is refused",
+    async (view, extra, sendButton) => {
+        const page = await bootPopup(profileNotRead(extra));
+        expect(page.visibleViews()).toEqual([view]);
+        // The dropdown's first option, which a browser selects by itself.
+        page.node("send-token").value = "ETH";
+
+        await page.click(sendButton);
+
+        expect(page.visibleViews()).toEqual(["send"]);
+        expect(page.text("send-balance")).toBe(
+            "Current balance: unknown (ETH)",
+        );
+
+        await page.click("btn-send-max");
+
+        expect(page.text("flash-msg")).toBe("This token's balance is unknown.");
+
+        await page.click("btn-send-back");
+        const { refreshBalances } = require("../src/shared/balances");
+        refreshBalances.mockImplementationOnce(async (wallets) => {
+            wallets[0].addresses[0].balance = "0.0";
+            return [];
+        });
+        await page.tick();
+        await page.click(sendButton);
+
+        expect(page.visibleViews()).toEqual([view]);
+        expect(page.text("flash-msg")).toBe("Cannot send — zero balance.");
+    },
+);
diff --git a/tests/addressValue.test.js b/tests/addressValue.test.js
index ea5fe0a..3e8833b 100644
--- a/tests/addressValue.test.js
+++ b/tests/addressValue.test.js
@@ -125,6 +125,14 @@ describe("the value of an address, and whether it is the whole value", () => {
         expect(getAddressValue(addr)).toEqual({ usd: 0, partial: false });
     });
 
+    // No total can include an ETH balance no refresh has read, and "unpriced
+    // tokens only" would be untrue of an address with nothing known at all.
+    test("an ETH balance no refresh has read means no value", () => {
+        const addr = { address: "0x1", balance: null, tokenBalances: [] };
+        expect(getAddressValue(addr)).toEqual({ usd: null, partial: false });
+        expect(formatAddressTotal(getAddressValue(addr))).toBe("");
+    });
+
     // Before the first price fetch, and on testnet, nothing is knowable: that
     // is a third state, and it stays distinct from both of the others.
     test("no prices at all means no value, not an incomplete one", () => {
diff --git a/tests/backgroundStateIsolation.test.js b/tests/backgroundStateIsolation.test.js
index 3ea75c9..4802e7c 100644
--- a/tests/backgroundStateIsolation.test.js
+++ b/tests/backgroundStateIsolation.test.js
@@ -445,7 +445,7 @@ describe("a balance refresh under a network switch", () => {
 
         const after = bg.persisted();
         expect(after.networkId).toBe("mainnet");
-        expect(after.wallets[0].addresses[0].balance).toBe("0");
+        expect(after.wallets[0].addresses[0].balance).toBeNull();
         expect(after.lastBalanceRefresh).toBe(0);
 
         await bg.fireBalanceAlarm();
diff --git a/tests/balanceRefreshNetworkSwitch.test.js b/tests/balanceRefreshNetworkSwitch.test.js
index 920a6f8..b548e84 100644
--- a/tests/balanceRefreshNetworkSwitch.test.js
+++ b/tests/balanceRefreshNetworkSwitch.test.js
@@ -70,7 +70,7 @@ async function chooseNetwork(page, networkId) {
 function expectNothingStored(page) {
     const stored = page.storage.read("autistmask");
     expect(stored.networkId).toBe("sepolia");
-    expect(stored.wallets[0].addresses[0].balance).toBe("0");
+    expect(stored.wallets[0].addresses[0].balance).toBeNull();
     expect(stored.wallets[0].addresses[0].tokenBalances).toEqual([]);
     expect(stored.lastBalanceRefresh).toBe(0);
 }
@@ -86,13 +86,13 @@ test("a refresh that returns after a switch in Settings writes nothing, and the
     await chooseNetwork(page, "sepolia");
     await refresh.finish();
 
-    expect(state.wallets[0].addresses[0].balance).toBe("0");
+    expect(state.wallets[0].addresses[0].balance).toBeNull();
     expect(state.wallets[0].addresses[0].tokenBalances).toEqual([]);
     expectNothingStored(page);
 
     await page.click("btn-settings-back");
     expect(page.visibleViews()).toEqual(["main"]);
-    expect(page.text("total-value")).toBe("0.0000 SepoliaETH");
+    expect(page.text("total-value")).toBe("unknown (SepoliaETH)");
 
     await page.tick();
 
@@ -138,7 +138,7 @@ test("a refresh whose save is reading the stored record when the user switches i
     await page.settle();
 
     expect(state.networkId).toBe("sepolia");
-    expect(state.wallets[0].addresses[0].balance).toBe("0");
+    expect(state.wallets[0].addresses[0].balance).toBeNull();
     expect(state.wallets[0].addresses[0].tokenBalances).toEqual([]);
     expectNothingStored(page);
 });
@@ -166,11 +166,11 @@ test("a refresh that returns after the background switched the network writes no
 });
 
 // The background's refresh saves Ethereum Mainnet's balances while the switch
-// in Settings waits for the lock. This page last saved a balance of "0" and no
+// in Settings waits for the lock. This page last saved a balance of null and no
 // token balances, the values that the switch sets.
 test("a background refresh saved while a switch in Settings waits for the lock leaves none of its balances stored", async () => {
     const profile = unversionedValidProfile();
-    profile.wallets[0].addresses[0].balance = "0";
+    profile.wallets[0].addresses[0].balance = null;
     const page = await bootPopup(profile);
     expect(page.pageErrors).toEqual([]);
     const background = require("../src/background/state");
diff --git a/tests/chainSwitchGate.test.js b/tests/chainSwitchGate.test.js
index da0a097..da240c0 100644
--- a/tests/chainSwitchGate.test.js
+++ b/tests/chainSwitchGate.test.js
@@ -328,7 +328,7 @@ describe("only the user switches the network", () => {
         const after = bg.walletState();
         expect(after.networkId).toBe("sepolia");
         expect(after.rpcUrl).toBe(SEPOLIA.defaultRpcUrl);
-        expect(after.wallets[0].addresses[0].balance).toBe("0");
+        expect(after.wallets[0].addresses[0].balance).toBeNull();
         expect(bg.chainChangedEvents()).toEqual([
             {
                 type: "AUTISTMASK_EVENT",
diff --git a/tests/coldWorkerChainSwitch.test.js b/tests/coldWorkerChainSwitch.test.js
index a89a2f7..60b1d53 100644
--- a/tests/coldWorkerChainSwitch.test.js
+++ b/tests/coldWorkerChainSwitch.test.js
@@ -39,7 +39,7 @@ function walletFixture() {
         {
             name: "Wallet 1",
             type: "hd",
-            addresses: [{ address: ADDRESS, balance: "0", tokenBalances: [] }],
+            addresses: [{ address: ADDRESS, balance: null, tokenBalances: [] }],
         },
     ];
 }
diff --git a/tests/deleteAddress.test.js b/tests/deleteAddress.test.js
index 5d04911..42b157a 100644
--- a/tests/deleteAddress.test.js
+++ b/tests/deleteAddress.test.js
@@ -33,6 +33,7 @@ const USDC = "0xa0b86991c6218b36c1d19d4a2e9eb0ce3606eb48";
 const EMPTY = { address: "0x1", balance: "0.0000", tokenBalances: [] };
 const ETH_ONLY = { address: "0x1", balance: "1.5", tokenBalances: [] };
 const DUST = { address: "0x1", balance: "0.00001", tokenBalances: [] };
+const NOT_READ = { address: "0x1", balance: null, tokenBalances: [] };
 const TOKEN_ONLY = {
     address: "0x1",
     balance: "0.0000",
@@ -106,14 +107,23 @@ describe("whether an address holds anything", () => {
         expect(addressHoldsFunds(DUST)).toBe(true);
     });
 
+    // No refresh has read it, so the address may hold funds.
+    test("an ETH balance no refresh has read counts", () => {
+        expect(addressHoldsFunds(NOT_READ)).toBe(true);
+    });
+
     test("an address holding nothing does not", () => {
         expect(addressHoldsFunds(EMPTY)).toBe(false);
         expect(addressHoldsFunds(ZERO_TOKEN)).toBe(false);
     });
 
-    test("a missing address or missing fields do not", () => {
+    test("a missing address does not", () => {
         expect(addressHoldsFunds(undefined)).toBe(false);
-        expect(addressHoldsFunds({ address: "0x1" })).toBe(false);
+    });
+
+    // It reads as unknown, as a null balance does.
+    test("an address with no ETH balance field counts", () => {
+        expect(addressHoldsFunds({ address: "0x1" })).toBe(true);
     });
 });
 
@@ -140,6 +150,20 @@ describe("the balance warning on the removal confirmation", () => {
         expect(html).toContain("<span>0.0000</span>");
     });
 
+    test("an ETH balance no refresh has read is warned about, and reads as unknown", () => {
+        const html = balanceWarningHtml(NOT_READ);
+        expect(html).toContain("This address may hold a balance.");
+        expect(html).not.toContain("This address holds a balance.");
+        expect(html).toContain("quantity unknown");
+        expect(html).not.toContain("0.0000");
+    });
+
+    test("an address with no ETH balance field reads the same", () => {
+        expect(balanceWarningHtml({ address: "0x1" })).toContain(
+            "This address may hold a balance.",
+        );
+    });
+
     // The sentence must not assert an amount, because any amount it could
     // assert has been rounded: "This address holds 0.0000 ETH." is what the
     // rounded form produces for an address that holds real money.
diff --git a/tests/popupFollowsNetworkSwitch.test.js b/tests/popupFollowsNetworkSwitch.test.js
index bf1b293..2f186d9 100644
--- a/tests/popupFollowsNetworkSwitch.test.js
+++ b/tests/popupFollowsNetworkSwitch.test.js
@@ -134,7 +134,7 @@ test.each([
     await backgroundSwitch(page, "sepolia");
 
     expect(page.visibleViews()).toEqual(["main"]);
-    expect(page.text("total-value")).toBe("0.0000 SepoliaETH");
+    expect(page.text("total-value")).toBe("unknown (SepoliaETH)");
 });
 
 // A request on Ethereum Mainnet fails, so Home's list holds the failure message.
diff --git a/tests/sendMax.test.js b/tests/sendMax.test.js
index cd64adb..c7535ff 100644
--- a/tests/sendMax.test.js
+++ b/tests/sendMax.test.js
@@ -432,6 +432,27 @@ describe("Max on an ETH send", () => {
         },
     );
 
+    test("says so when no refresh has read the ETH balance", async () => {
+        await refreshWith(BALANCE_WEI);
+        state.wallets[0].addresses[0].balance = null;
+        openSend();
+        await pressMax();
+        expect(el("send-amount").value).toBe("");
+        expect(text("flash-msg")).toBe("This token's balance is unknown.");
+    });
+
+    test("fills nothing in and says nothing when a network switch cleared the balance while the fee was estimated", async () => {
+        await refreshWith(BALANCE_WEI);
+        openSend();
+        const release = holdFeeEstimate();
+        const pressed = pressMax();
+        state.wallets[0].addresses[0].balance = null;
+        release();
+        await pressed;
+        expect(el("send-amount").value).toBe("");
+        expect(text("flash-msg")).toBe("");
+    });
+
     test("fills nothing in and says nothing once Send was left while the fee was estimated", async () => {
         // 0.0001 ETH, which does not cover the fee: a result that landed
         // would say so on whichever screen is shown.