diff --git a/README.md b/README.md
index 98485d7..e540937 100644
--- a/README.md
+++ b/README.md
@@ -464,6 +464,9 @@ papered over:
   forced by clicking Reveal and the settings gear in one page task, which a
   person cannot do; the case a person can hit, the first decrypt after the popup
   opens while libsodium is still loading, is not driven.
+- Approval windows open at 1280x720 whatever size the extension asks for, so
+  whether an approval screen fits its window is checked in the Firefox suite
+  only.
 
 Any test that drives a failure path on purpose declares the `console.error` it
 is about to provoke, via `errors.expect()`. That is not a mute: the declaration
@@ -536,7 +539,8 @@ suite), wallet creation through the UI, the Add Token screen, and the dApp round
 trips — `eth_requestAccounts`, `personal_sign`, `wallet_switchEthereumChain`
 rejected and then approved, `eth_sendTransaction`, and a closed approval window
 rejecting with EIP-1193 4001 — driven through the real content script,
-background page and approval windows.
+background page and approval windows. The `personal_sign` prompt is also
+required to fit its window without scrolling sideways.
 
 The suite lives in `tests/e2e/firefox/`. Its WebDriver client (`driver.js`) has
 **no npm dependencies at all**: it is built on global `fetch` and
@@ -893,8 +897,11 @@ discoverable.
   enough that vanilla JS with simple view switching is sufficient. A framework
   would add bundle size, build complexity, and attack surface for no benefit at
   this scale.
-- **360x600 popup**: Standard browser extension popup dimensions. The UI is
-  designed for this fixed viewport.
+- **396x600 popup**: The page is 396 pixels wide (`body` in
+  `src/popup/styles/main.css`), and 600 pixels is as tall as the browser lets
+  the toolbar popup grow. The UI is designed for this fixed viewport. The window
+  an approval opens in is given the same size; the browser counts the window's
+  frame in its width, so the page widens the window by whatever the frame takes.
 
 #### No Layout Shift
 
diff --git a/src/background/index.js b/src/background/index.js
index 00fa439..c589f92 100644
--- a/src/background/index.js
+++ b/src/background/index.js
@@ -423,7 +423,10 @@ function releaseApproval(approval) {
 // the result on the floor, so a rejection here would be unhandled.
 async function openApprovalWindow(id) {
     const popupUrl = runtime.getURL("src/popup/index.html?approval=" + id);
-    const popupWidth = 360;
+    // As wide as the page: body in src/popup/styles/main.css. The browser
+    // counts the window's frame in this width; the page itself adds back
+    // whatever the frame takes (src/popup/index.js).
+    const popupWidth = 396;
     const popupHeight = 600;
 
     let currentWin = null;
@@ -443,7 +446,7 @@ async function openApprovalWindow(id) {
     // Centred on a browser window only. The last focused window can be
     // another approval window still open, and centring on one can give a
     // position the browser refuses ("Bounds must be at least 50% within
-    // visible screen space"): headless Chrome reports this 360x600 popup as
+    // visible screen space"): headless Chrome reports this 396x600 popup as
     // 1280x720. The request then failed with no window at all. Over a popup,
     // the browser picks the position.
     if (currentWin && currentWin.type === "normal") {
diff --git a/src/popup/index.js b/src/popup/index.js
index 6999cc9..df72634 100644
--- a/src/popup/index.js
+++ b/src/popup/index.js
@@ -21,6 +21,7 @@ const {
     goBack,
 } = require("./views/helpers");
 const { applyTheme } = require("./theme");
+const { windowsGetCurrent, windowsUpdate } = require("../shared/browserApi");
 // Renders a view the popup lands on without having navigated to it forward:
 // on restore here, and on Back. Only the views that can be fully re-rendered
 // from persisted state (RESTORABLE_VIEWS, src/shared/restorableViews.js) go
@@ -233,6 +234,22 @@ async function init() {
     const params = new URLSearchParams(window.location.search);
     const approvalId = params.get("approval");
     if (approvalId) {
+        // The background opens this window as wide as the page, but the
+        // browser counts the window's frame in that width, and how wide the
+        // frame is depends on the browser and the system. The window is
+        // widened by however far the page would scroll sideways. The
+        // connection prompt can also show in the toolbar popup, whose window
+        // is the user's browser window; that one is left alone.
+        const sideways =
+            document.documentElement.scrollWidth -
+            document.documentElement.clientWidth;
+        if (sideways > 0) {
+            windowsGetCurrent().then((win) => {
+                if (win.type === "popup") {
+                    windowsUpdate(win.id, { width: win.width + sideways });
+                }
+            });
+        }
         // Deliberately not awaited, and deliberately not .catch()ed. show()
         // is async, so a throw past its first await surfaces as an unhandled
         // rejection rather than an uncaught error — measured as still failing
diff --git a/src/shared/browserApi.js b/src/shared/browserApi.js
index c512286..1122afe 100644
--- a/src/shared/browserApi.js
+++ b/src/shared/browserApi.js
@@ -250,6 +250,22 @@ function windowsGetLastFocused() {
     return invoke(windowsApi(), "getLastFocused");
 }
 
+/**
+ * @returns {Promise<Object>} the window the calling page is in.
+ */
+function windowsGetCurrent() {
+    return invoke(windowsApi(), "getCurrent");
+}
+
+/**
+ * @param {number} windowId
+ * @param {Object} updateInfo
+ * @returns {Promise<Object>} the updated window.
+ */
+function windowsUpdate(windowId, updateInfo) {
+    return invoke(windowsApi(), "update", windowId, updateInfo);
+}
+
 /**
  * @param {number} windowId
  * @returns {Promise<void>}
@@ -275,6 +291,8 @@ module.exports = {
     tabsSendMessage,
     windowsApi,
     windowsCreate,
+    windowsGetCurrent,
     windowsGetLastFocused,
     windowsRemove,
+    windowsUpdate,
 };
diff --git a/tests/approvalWindow.test.js b/tests/approvalWindow.test.js
index 6f81442..58522f0 100644
--- a/tests/approvalWindow.test.js
+++ b/tests/approvalWindow.test.js
@@ -45,3 +45,50 @@ test("the approval window shows no screen until the background describes the app
     expect(env.visibleViews()).toEqual(["approve-network"]);
     expect(env.pageErrors).toEqual([]);
 });
+
+// The background opens the approval window as wide as the page, but the
+// browser counts the window's frame in that width
+// (https://git.eeqj.de/sneak/AutistMask/issues/518). The browser suites run
+// without frames, so the widening is checked here.
+function windowsStub(type) {
+    const updates = [];
+    return {
+        updates,
+        getCurrent: (done) => done({ id: 7, type, width: 396 }),
+        update: (id, info, done) => {
+            updates.push({ id, info });
+            done({});
+        },
+    };
+}
+
+const approvalRuntime = {
+    connect: () => ({ postMessage: () => {} }),
+    sendMessage: () => {},
+};
+
+test("the approval window widens itself by whatever its frame takes", async () => {
+    const windows = windowsStub("popup");
+    const env = await bootPopup(unversionedValidProfile(), {
+        search: "?approval=approval-1",
+        runtime: approvalRuntime,
+        windows,
+        documentElement: { scrollWidth: 396, clientWidth: 380 },
+    });
+
+    expect(windows.updates).toEqual([{ id: 7, info: { width: 412 } }]);
+    expect(env.pageErrors).toEqual([]);
+});
+
+test("a connection prompt in the toolbar popup leaves the browser window alone", async () => {
+    const windows = windowsStub("normal");
+    const env = await bootPopup(unversionedValidProfile(), {
+        search: "?approval=approval-1",
+        runtime: approvalRuntime,
+        windows,
+        documentElement: { scrollWidth: 396, clientWidth: 380 },
+    });
+
+    expect(windows.updates).toEqual([]);
+    expect(env.pageErrors).toEqual([]);
+});
diff --git a/tests/backgroundApproval.test.js b/tests/backgroundApproval.test.js
index f0ad395..9a4cc3d 100644
--- a/tests/backgroundApproval.test.js
+++ b/tests/backgroundApproval.test.js
@@ -2805,7 +2805,7 @@ describe("where an approval window opens", () => {
         await settle();
 
         expect(bg.created).toHaveLength(1);
-        expect(bg.created[0]).toMatchObject({ left: 460, top: 60 });
+        expect(bg.created[0]).toMatchObject({ left: 442, top: 60 });
     });
 
     test("not centred on an approval window the user was last in", async () => {
@@ -2822,7 +2822,7 @@ describe("where an approval window opens", () => {
         bg.requestSign();
         await settle();
 
-        // Centred, it would be at left 900, the position the browser refused.
+        // Centred, it would be at left 882, the position the browser refused.
         expect(bg.created).toHaveLength(1);
         expect(bg.created[0].left).toBeUndefined();
         expect(bg.created[0].top).toBeUndefined();
@@ -2844,7 +2844,7 @@ describe("where an approval window opens", () => {
         await settle();
 
         expect(bg.created).toHaveLength(2);
-        expect(bg.created[0]).toMatchObject({ left: 1520, top: 750 });
+        expect(bg.created[0]).toMatchObject({ left: 1502, top: 750 });
         expect(bg.created[1].left).toBeUndefined();
         expect(bg.created[1].top).toBeUndefined();
 
diff --git a/tests/e2e/firefox/run.js b/tests/e2e/firefox/run.js
index 14d6f31..e6a4df2 100644
--- a/tests/e2e/firefox/run.js
+++ b/tests/e2e/firefox/run.js
@@ -640,6 +640,19 @@ step(
         await d.switchToWindow(popup);
         await d.waitVisible("#view-approve-sign");
 
+        // The window is opened as wide as the page
+        // (https://git.eeqj.de/sneak/AutistMask/issues/518). This suite is
+        // where that is checked: the Chrome suite's approval windows open at
+        // 1280x720 whatever width the extension asks for.
+        const sideways = await d.execute(
+            "return document.documentElement.scrollWidth -" +
+                " document.documentElement.clientWidth;",
+        );
+        assert(
+            sideways <= 0,
+            "the sign prompt scrolls sideways by " + sideways + "px",
+        );
+
         const screen = await d.execute(
             `return {
              origin: document.getElementById("approve-sign-origin").textContent,
diff --git a/tests/support/popupBoot.js b/tests/support/popupBoot.js
index 308d0d4..93d0dcc 100644
--- a/tests/support/popupBoot.js
+++ b/tests/support/popupBoot.js
@@ -242,6 +242,11 @@ async function settle() {
  *     "?approval=" and an id for the popup opened as an approval window.
  * @param {object} [options.runtime] members of chrome.runtime that replace the
  *     stub's own, for a test that has to answer the background's messages.
+ * @param {object} [options.windows] chrome.windows, for a test of the approval
+ *     window resizing itself.
+ * @param {object} [options.documentElement] members of document.documentElement
+ *     that replace the stub's own: scrollWidth and clientWidth, which are equal
+ *     unless a test says otherwise, so the page does not scroll sideways.
  * @returns {Promise<object>} handles onto the booted page.
  */
 async function bootPopup(stored, options) {
@@ -277,6 +282,11 @@ async function bootPopup(stored, options) {
         (options && options.storage) ||
         makeStorageStub(stored === undefined ? {} : { autistmask: stored });
     const document = makeDocument(POPUP_HTML);
+    Object.assign(
+        document.documentElement,
+        { scrollWidth: 396, clientWidth: 396 },
+        options && options.documentElement,
+    );
     const reloads = [];
 
     globalThis.chrome = {
@@ -287,6 +297,7 @@ async function bootPopup(stored, options) {
             onMessage: { addListener: () => {} },
             ...(options && options.runtime),
         },
+        windows: options && options.windows,
     };
     globalThis.document = document;
     globalThis.window = {