diff --git a/README.md b/README.md
index 5f5bd87..9a9ef4a 100644
--- a/README.md
+++ b/README.md
@@ -1251,8 +1251,14 @@ A V4 step with no swap action sets only the sides its `SETTLE`, `SETTLE_ALL`,
 `TAKE` or `TAKE_ALL` names.
 
 An `UNWRAP_WETH` step makes `Token Out` ETH only when the output side is WETH,
-on mainnet or Sepolia, or when no step set the output side; a WETH
-`Min. received` figure then reads in ETH. Otherwise `Token Out` and
+on mainnet or Sepolia, that the router holds when the step runs (Transaction
+Decoding below gives what the router holds), or when no step set the output
+side; a WETH `Min. received` figure then reads in ETH. A later step that sets
+the output side sets it anew. The router unwraps only the WETH it holds, so a
+swap that pays its WETH to the user and then unwraps shows WETH. The decoder
+follows what the router holds by token, not by step: a swap that pays part of
+its WETH to the user and part to the router, and then unwraps, shows ETH with
+the minimum of the step that set the output side. Otherwise `Token Out` and
 `Min. received` keep the output side's own token and figure, whether the swap
 was paid in ETH or in a token: a V2 exact-out swap that buys USDC and then
 unwraps the WETH it did not spend shows USDC. The token permission warning on
diff --git a/src/shared/uniswap.js b/src/shared/uniswap.js
index 3f9177d..e29755f 100644
--- a/src/shared/uniswap.js
+++ b/src/shared/uniswap.js
@@ -1219,6 +1219,10 @@ function decode(data, toAddress, chainId, sources, fromAddress) {
         let minOutput = null;
         let outputEstablished = false;
         let hasUnwrapWeth = false;
+        // Set when an UNWRAP_WETH pays out, as ETH, the output side's WETH,
+        // which the router holds; cleared whenever the output side is set
+        // again.
+        let outputUnwrapped = false;
         let hasV2OrV3ExactOut = false;
         let swapUndecoded = false;
         let hasSubPlan = false;
@@ -1260,6 +1264,7 @@ function decode(data, toAddress, chainId, sources, fromAddress) {
             outputToken = present(token) ? token : null;
             minOutput = present(amount) ? amount : null;
             outputEstablished = true;
+            outputUnwrapped = false;
         };
 
         // What the steps take from the sender beyond the amount of the step
@@ -1744,6 +1749,7 @@ function decode(data, toAddress, chainId, sources, fromAddress) {
                         outputToken = v4.tokenOut;
                         minOutput = v4.amountOutMin;
                         outputEstablished = true;
+                        outputUnwrapped = false;
                     } else if (v4) {
                         // A step with no swap action sets only the sides its
                         // SETTLE, SETTLE_ALL, TAKE or TAKE_ALL names:
@@ -1772,6 +1778,17 @@ function decode(data, toAddress, chainId, sources, fromAddress) {
                     }
                 } else if (command === "UNWRAP_WETH") {
                     hasUnwrapWeth = true;
+                    // The router unwraps all the WETH it holds, the output
+                    // side's included when it is WETH the router holds, even
+                    // when the recipient cannot be read. WETH a step paid to
+                    // anyone else is not unwrapped.
+                    if (
+                        present(outputToken) &&
+                        WETH_ADDRESSES.includes(outputToken.toLowerCase()) &&
+                        heldByRouter.has(outputToken.toLowerCase())
+                    ) {
+                        outputUnwrapped = true;
+                    }
                     const u = decodeUnwrapWeth(inputs[i]);
                     if (u) {
                         addPayee(u.recipient);
@@ -1912,23 +1929,22 @@ function decode(data, toAddress, chainId, sources, fromAddress) {
             outputToken = null;
             minOutput = null;
             outputEstablished = true;
+            outputUnwrapped = false;
         }
 
         // Resolve token info. A null token on either side means no step named
         // a currency for it, a V4 step with a swap action left it unknown, or
         // an EXECUTE_SUB_PLAN step did; tokenInfo() refuses rather than calling
         // it ETH. UNWRAP_WETH turns WETH into ETH, so it makes the output ETH
-        // when the output side is WETH, or when no step set the output side. A
-        // V4 step with a swap action, or an EXECUTE_SUB_PLAN step, did set it,
-        // even when it set it unknown. Any other output keeps its own token
-        // and figure: a swap that buys USDC and then unwraps the WETH it did
-        // not spend receives USDC.
-        const outputIsWeth =
-            present(outputToken) &&
-            WETH_ADDRESSES.includes(outputToken.toLowerCase());
+        // when it unwraps the output side's WETH (`outputUnwrapped`), or when
+        // no step set the output side. A V4 step with a swap action, or
+        // an EXECUTE_SUB_PLAN step, did set it, even when it set it unknown.
+        // Any other output keeps its own token and figure: a swap that pays
+        // its WETH to the user and then unwraps receives WETH, and one that
+        // buys USDC and then unwraps the WETH it did not spend receives USDC.
         const inInfo = tokenInfo(inputToken, sources);
         const outInfo =
-            hasUnwrapWeth && (outputIsWeth || !outputEstablished)
+            outputUnwrapped || (hasUnwrapWeth && !outputEstablished)
                 ? { symbol: "ETH", decimals: 18, address: null }
                 : tokenInfo(outputToken, sources);
 
diff --git a/tests/uniswap.test.js b/tests/uniswap.test.js
index 277201f..9144d6a 100644
--- a/tests/uniswap.test.js
+++ b/tests/uniswap.test.js
@@ -875,7 +875,7 @@ describe("uniswap decoder", () => {
         const data = buildExecute(
             solidityPacked(["uint8", "uint8"], [0x08, 0x0c]),
             [
-                encodeV2SwapExactIn(USER_ADDR, 1000000n, 500000000000000n, [
+                encodeV2SwapExactIn(ROUTER_ADDR, 1000000n, 500000000000000n, [
                     USDC_ADDR,
                     SEPOLIA_WETH_ADDR,
                 ]),
@@ -958,7 +958,7 @@ describe("uniswap decoder", () => {
         const data = buildExecute(
             solidityPacked(["uint8", "uint8"], [0x08, 0x0c]),
             [
-                encodeV2SwapExactIn(USER_ADDR, 1000000n, 500000000000000n, [
+                encodeV2SwapExactIn(ROUTER_ADDR, 1000000n, 500000000000000n, [
                     USDT_ADDR,
                     WETH_ADDR,
                 ]),
diff --git a/tests/uniswapRecipient.test.js b/tests/uniswapRecipient.test.js
index fc4c786..fdedc12 100644
--- a/tests/uniswapRecipient.test.js
+++ b/tests/uniswapRecipient.test.js
@@ -7,9 +7,11 @@
 // (https://git.eeqj.de/sneak/AutistMask/issues/592), the address whose
 // balance a BALANCE_CHECK_ERC20 checks
 // (https://git.eeqj.de/sneak/AutistMask/issues/600), any token a swap
-// leaves in the router (https://git.eeqj.de/sneak/AutistMask/issues/606), and
+// leaves in the router (https://git.eeqj.de/sneak/AutistMask/issues/606),
 // what each PERMIT2_TRANSFER_FROM moves
-// (https://git.eeqj.de/sneak/AutistMask/issues/611).
+// (https://git.eeqj.de/sneak/AutistMask/issues/611), and when an
+// UNWRAP_WETH makes the output ETH
+// (https://git.eeqj.de/sneak/AutistMask/issues/607).
 //
 // Every swap command, SWEEP, WRAP_ETH, UNWRAP_WETH, TRANSFER, PAY_PORTION,
 // PAY_PORTION_FULL_PRECISION, PERMIT2_TRANSFER_FROM, ACROSS_V4_DEPOSIT_V3 and
@@ -531,7 +533,7 @@ describe("an output left in the router is not received", () => {
         {
             kind: "an UNWRAP_WETH to the user, then the swap",
             data: execute(unwrapWeth(MSG_SENDER), toRouter),
-            min: "1.0000 ETH",
+            min: "1.0000 WETH",
         },
         {
             kind: "the swap, then a WRAP_ETH of zero to the user",
@@ -568,6 +570,64 @@ describe("an output left in the router is not received", () => {
     });
 });
 
+// https://git.eeqj.de/sneak/AutistMask/issues/607: an UNWRAP_WETH pays out,
+// as ETH, the WETH the router holds when it runs. Token Out read ETH whenever
+// the output side was WETH, so a swap that paid its WETH to the user before
+// the UNWRAP_WETH read as ETH, though the user receives WETH.
+describe("an UNWRAP_WETH makes the output ETH only when the router holds it", () => {
+    test("a swap paying its WETH to the user, then an UNWRAP_WETH, reads as WETH", () => {
+        const result = decode(
+            execute(swapToWeth(MSG_SENDER), unwrapWeth(MSG_SENDER)),
+        );
+        expect(result.name).toBe("Swap USDT → WETH");
+        expect(labels(result)).toEqual(PAID_TO_USER);
+        expect(detail(result, "Min. received").value).toBe("1.0000 WETH");
+    });
+
+    test("a swap paying its WETH to the router, then an UNWRAP_WETH to the user, reads as ETH", () => {
+        const result = decode(
+            execute(swapToWeth(ADDRESS_THIS), unwrapWeth(MSG_SENDER)),
+        );
+        expect(result.name).toBe("Swap USDT → ETH");
+        expect(labels(result)).toEqual(PAID_TO_USER);
+        expect(detail(result, "Min. received").value).toBe("1.0000 ETH");
+    });
+
+    // The user receives the first step's WETH as WETH and the second's as
+    // ETH. The second step sets the output side, and the router holds its
+    // WETH, so the output reads as ETH with the second step's minimum.
+    test("a swap paying part of its WETH to the user and the rest to the router, then an UNWRAP_WETH, reads as ETH", () => {
+        const result = decode(
+            execute(
+                swapToWeth(MSG_SENDER),
+                v2Swap(0x08, ADDRESS_THIS, USDC_1990, ONE_WETH / 2n, [
+                    USDC,
+                    WETH,
+                ]),
+                unwrapWeth(MSG_SENDER),
+            ),
+        );
+        expect(result.name).toBe("Swap USDT → ETH");
+        expect(detail(result, "Min. received").value).toBe("0.5000 ETH");
+    });
+
+    // A step after the UNWRAP_WETH that sets the output side sets it anew.
+    test("a swap paying WETH to the user after an UNWRAP_WETH of an earlier swap's WETH reads as WETH", () => {
+        const result = decode(
+            execute(
+                swapToWeth(ADDRESS_THIS),
+                unwrapWeth(MSG_SENDER),
+                v2Swap(0x08, MSG_SENDER, USDC_1990, ONE_WETH / 2n, [
+                    USDC,
+                    WETH,
+                ]),
+            ),
+        );
+        expect(result.name).toBe("Swap USDT → WETH");
+        expect(detail(result, "Min. received").value).toBe("0.5000 WETH");
+    });
+});
+
 // https://git.eeqj.de/sneak/AutistMask/issues/606: any token a step pays the
 // router stays there unless a later step pays out or spends all of it, not
 // only the swap's output. A V4 SETTLE can take more of the user's tokens than