diff --git a/README.md b/README.md
index 63e2994..e20ba2b 100644
--- a/README.md
+++ b/README.md
@@ -1277,22 +1277,18 @@ see Transaction Decoding), do not always read as a number. They can read:
   step pays nothing itself and swaps whatever an earlier step sent to the pair,
   so the calldata states no quantity. A V3 exact-in `amountIn` of zero has no
   such meaning and is shown as a zero.
-- `None (no minimum guaranteed)`: the swap's `Min. received` line, when the
-  minimum it shows is zero, whether a V2, V3 or V4 swap's minimum or a
-  `BALANCE_CHECK_ERC20` step's `minBalance`. Before
-  [#359](https://git.eeqj.de/sneak/AutistMask/issues/359), a zero `minBalance`
-  read `0.0000` when the token's scale was known. The router passes a balance
-  check whenever the balance is at least `minBalance`, so a zero `minBalance`
-  guarantees nothing: it sets `Token Out` and `Min. received` only when the
-  output side holds no minimum, not even a zero one, at the point the check is
-  reached, and otherwise leaves the current token and figure in place. A nonzero
-  `minBalance` sets both lines, as a swap step does. Only a check of the
-  transaction's sender's own balance sets either line; a check of any other
-  address sets neither (see Transaction Decoding). A `BALANCE_CHECK_ERC20` step
-  that the router lets fail without reverting the transaction (see Transaction
-  Decoding) guarantees nothing either, whatever its `minBalance`, and is read as
-  one whose `minBalance` is zero. A minimum stated by a V4 swap step the router
-  lets fail is likewise read as zero.
+- `None (no minimum guaranteed)`: the swap's `Min. received` line, when it shows
+  a V2, V3 or V4 swap's minimum of zero. The router passes a
+  `BALANCE_CHECK_ERC20` step whenever the balance is at least `minBalance`, so a
+  zero `minBalance` guarantees nothing. A check with a zero `minBalance` sets
+  neither `Token Out` nor `Min. received`. A nonzero `minBalance` sets both
+  lines, as a swap step does. Only a check of the transaction's sender's own
+  balance sets either line; a check of any other address sets neither (see
+  Transaction Decoding). A `BALANCE_CHECK_ERC20` step that the router lets fail
+  without reverting the transaction (see Transaction Decoding) guarantees
+  nothing either, whatever its `minBalance`, and is read as one whose
+  `minBalance` is zero. A minimum stated by a V4 swap step the router lets fail
+  is likewise read as zero.
 
 The swap's `Token In` and `Token Out` lines name a currency, not an amount; each
 reads `Unknown (not named in the calldata)` when the decoder found no token for
@@ -3397,7 +3393,8 @@ Currently supported:
   `Balance Check (of another address)`. A check whose input does not decode,
   such as one whose owner word has a nonzero top byte (the router reads the
   owner from the word's last 20 bytes), likewise sets neither, and it is listed
-  as `Balance Check (could not be decoded)`. When a swap step, `TAKE` or
+  as `Balance Check (could not be decoded)`. A check with a zero `minBalance`
+  sets neither `Token Out` nor the minimum. When a swap step, `TAKE` or
   `TAKE_PORTION` pays the router any token, the swap's output or another, a
   `WRAP_ETH` pays it WETH, or an `UNWRAP_WETH` into the router turns WETH a step
   paid it into ETH, that token stays in the router unless a later step pays out
diff --git a/src/shared/uniswap.js b/src/shared/uniswap.js
index 5e98da6..6e140b7 100644
--- a/src/shared/uniswap.js
+++ b/src/shared/uniswap.js
@@ -1629,13 +1629,13 @@ function decode(data, toAddress, chainId, sources, fromAddress) {
                     } else {
                         // The router passes this check whenever the owner
                         // holds at least minBalance, so a zero one guarantees
-                        // nothing and does not replace a minimum an earlier
-                        // step stated. A check the router lets fail guarantees
-                        // nothing either, so it is read as a zero one. Any
+                        // nothing. A check the router lets fail guarantees
+                        // nothing either, so it is read as a zero one. A zero
+                        // check sets neither Token Out nor the minimum. Any
                         // other minBalance sets the output side as a swap
-                        // does. It pays nobody.
+                        // does. The check pays nobody.
                         const minBalance = allowedToFail ? 0n : b.minBalance;
-                        if (!(minBalance === 0n && present(minOutput))) {
+                        if (minBalance !== 0n) {
                             setOutput(i, b.token, minBalance, []);
                         }
                         keepsRouterWeth = true;
diff --git a/tests/uniswap.test.js b/tests/uniswap.test.js
index 736c724..511f3ca 100644
--- a/tests/uniswap.test.js
+++ b/tests/uniswap.test.js
@@ -4380,10 +4380,9 @@ describe("uniswap decoder", () => {
         expect(detail(result, "Min. received").value).toBe("2.0000 USDC");
     });
 
-    // With no minimum stated before it, a zero balance check is what sets the
-    // output side, and it guarantees nothing. No step pays anyone, so the
-    // minimum is not said to be received.
-    test("a zero balance check with no earlier minimum states no minimum", () => {
+    // A zero balance check sets neither Token Out nor the minimum. The route
+    // pays only the WRAP_ETH's WETH, to the router, where it stays.
+    test("a zero balance check after a WRAP_ETH into the router names no output token and no minimum", () => {
         const data = buildExecute(
             solidityPacked(["uint8", "uint8"], [0x0b, 0x0e]),
             [
@@ -4396,9 +4395,16 @@ describe("uniswap decoder", () => {
         const result = uniswap.decode(data, ROUTER_ADDR, "0x1", {}, USER_ADDR);
         expect(result).not.toBeNull();
 
-        expect(detail(result, "Token Out").value).toContain("USDT");
-        expect(detail(result, "Min. paid out").value).toBe(
-            "None (no minimum guaranteed)",
+        expect(detail(result, "Token Out").value).toBe(
+            "Unknown (not named in the calldata)",
+        );
+        expect(detail(result, "Min. paid out")).toBeUndefined();
+        expect(detail(result, "Min. received")).toBeUndefined();
+        expect(detail(result, "Paid to").value).toBe(
+            "The router, where it stays (no later step pays it out)",
+        );
+        expect(detail(result, "Token moved into the router").address).toBe(
+            WETH_ADDR,
         );
     });
 
diff --git a/tests/uniswapRecipient.test.js b/tests/uniswapRecipient.test.js
index 4e9b9e6..548ee97 100644
--- a/tests/uniswapRecipient.test.js
+++ b/tests/uniswapRecipient.test.js
@@ -688,6 +688,62 @@ describe("an UNWRAP_WETH makes the output ETH only when the router holds it", ()
         ]);
     });
 
+    // The same route, then a balance check of the sender's USDC with a zero
+    // minimum. The check guarantees nothing, so Token Out stays ETH
+    // (https://git.eeqj.de/sneak/AutistMask/issues/649).
+    test("the same route, then a zero balance check of USDC, still reads as ETH with no minimum", () => {
+        const result = decode(
+            execute(
+                v4Swap(
+                    SWAP_USDT_FOR_WETH,
+                    SETTLE_USDT,
+                    take(WETH, MSG_SENDER, (ONE_WETH * 6n) / 10n),
+                    take(WETH, ADDRESS_THIS),
+                ),
+                unwrapWeth(MSG_SENDER),
+                balanceCheck(USDC, 0n),
+            ),
+        );
+        expect(result.name).toBe("Swap USDT → ETH");
+        expect(detail(result, "Token Out").value).toBe("ETH");
+        expect(labels(result)).toEqual([
+            "Protocol",
+            "Token In",
+            "Amount",
+            "Token Out",
+            "Steps",
+            "Deadline",
+        ]);
+    });
+
+    // A PERMIT2_TRANSFER_FROM moves the sender's WETH into the router. An
+    // UNWRAP_WETH pays that WETH to the user as ETH. A zero balance check of
+    // USDC sets neither Token Out nor the minimum, before the UNWRAP_WETH or
+    // after it (https://git.eeqj.de/sneak/AutistMask/issues/649).
+    test.each([
+        {
+            kind: "before the UNWRAP_WETH",
+            steps: [balanceCheck(USDC, 0n), unwrapWeth(MSG_SENDER)],
+        },
+        {
+            kind: "after the UNWRAP_WETH",
+            steps: [unwrapWeth(MSG_SENDER), balanceCheck(USDC, 0n)],
+        },
+    ])(
+        "WETH moved into the router and unwrapped, with a zero balance check of USDC $kind, reads as ETH with no minimum",
+        ({ steps }) => {
+            const result = decode(
+                execute(
+                    permit2TransferFrom(WETH, ADDRESS_THIS, ONE_WETH),
+                    ...steps,
+                ),
+            );
+            expect(detail(result, "Token Out").value).toBe("ETH");
+            expect(detail(result, "Min. received")).toBeUndefined();
+            expect(detail(result, "Min. paid out")).toBeUndefined();
+        },
+    );
+
     // A TAKE the decoder cannot read may pay part of the WETH to the user.
     test("one V4 step paying WETH to the router beside a TAKE that cannot be read, then an UNWRAP_WETH, reads as ETH with no minimum", () => {
         const result = decode(
@@ -2820,17 +2876,16 @@ describe("the allow-revert flag", () => {
         },
     );
 
-    test("a BALANCE_CHECK_ERC20 with the flag, and no minimum before it, states none", () => {
+    test("a BALANCE_CHECK_ERC20 with the flag, and no minimum before it, names no output token and no minimum", () => {
         const check = balanceCheck(WETH, ONE_WETH);
         expect(detail(decode(execute(check)), "Min. paid out").value).toBe(
             "1.0000 WETH",
         );
 
         const withFlag = decode(execute(flagged(check)));
-        expect(detail(withFlag, "Token Out").address).toBe(WETH);
-        expect(detail(withFlag, "Min. paid out").value).toBe(
-            "None (no minimum guaranteed)",
-        );
+        expect(detail(withFlag, "Token Out").value).toBe(UNNAMED);
+        expect(detail(withFlag, "Min. paid out")).toBeUndefined();
+        expect(detail(withFlag, "Min. received")).toBeUndefined();
     });
 
     // Only the routers from UniversalRouterV2 on let a PERMIT2_PERMIT fail.