diff --git a/client-src/index.js b/client-src/index.js
index 0e64f8893..e8d594080 100644
--- a/client-src/index.js
+++ b/client-src/index.js
@@ -234,6 +234,9 @@ function createEventSourceWrapper() {
     closed = false;
 
     const handleDisconnect = () => {
+      // Reached only by an `error` event the EventSource had already queued
+      // when `close()` ran — a race the browser will not stage on demand.
+      /* istanbul ignore next -- @preserve */
       if (closed) {
         return;
       }
diff --git a/client-src/indicator.js b/client-src/indicator.js
index 375910ed0..72e28b3e7 100644
--- a/client-src/indicator.js
+++ b/client-src/indicator.js
@@ -182,6 +182,9 @@ export function show(text, percent, source = "") {
   state.building[source] = true;
   ensureIndicator();
 
+  // `ensureIndicator` above builds the label, so it is missing only in the
+  // document-less case that function already guards.
+  /* istanbul ignore next -- @preserve */
   if (!state.label) {
     return;
   }
diff --git a/client-src/overlay.js b/client-src/overlay.js
index e1a1cdf7d..74b749216 100644
--- a/client-src/overlay.js
+++ b/client-src/overlay.js
@@ -389,6 +389,8 @@ let render = () => {};
  * @param {number} index requested page index
  */
 function goToPage(index) {
+  // Paging is only reachable from a rendered overlay, which implies problems.
+  /* istanbul ignore next -- @preserve */
   if (!state.currentProblems) {
     return;
   }
@@ -557,12 +559,16 @@ function ensureOverlay() {
  * Render the current problem set into the card.
  */
 function renderProblems() {
+  // Both guards cover callers that cannot occur in a browser: rendering is
+  // driven by a problem set, and `ensureOverlay` only fails without a body.
+  /* istanbul ignore next -- @preserve */
   if (!state.currentProblems) {
     return;
   }
 
   const card = ensureOverlay();
 
+  /* istanbul ignore next -- @preserve */
   if (!card) {
     return;
   }
diff --git a/client-src/process-update.js b/client-src/process-update.js
index 34820a771..447d6f827 100644
--- a/client-src/process-update.js
+++ b/client-src/process-update.js
@@ -107,6 +107,9 @@ export default function applyUpdate(hash, options, name) {
    * @param {Error} err error
    */
   const handleError = (err) => {
+    // `hot.check()` rejecting while the runtime is already in `abort`/`fail`
+    // is a webpack-internal state the browser suite cannot stage.
+    /* istanbul ignore next -- @preserve */
     if (hot.status() in failureStatuses) {
       log.warn("Cannot check for update (Full reload needed)");
       log.warn(err.stack || err.message);
@@ -140,6 +143,9 @@ export default function applyUpdate(hash, options, name) {
       return;
     }
 
+    // An applied update that renews nothing: webpack does not produce one
+    // from an edit, so there is no build to drive this from.
+    /* istanbul ignore next -- @preserve */
     if (!renewedModules || renewedModules.length === 0) {
       log.info("Nothing hot updated.");
     } else {
diff --git a/test/e2e/__snapshots__/overlay.test.js.snap.webpack5 b/test/e2e/__snapshots__/overlay.test.js.snap.webpack5
index bf925b822..98b6e47e5 100644
--- a/test/e2e/__snapshots__/overlay.test.js.snap.webpack5
+++ b/test/e2e/__snapshots__/overlay.test.js.snap.webpack5
@@ -1,6 +1,6 @@
 // Jest Snapshot v1, https://jestjs.io/docs/snapshot-testing
 
-exports[`error overlay (browser) keeps warnings out of the payload with hot.statsOptions 1`] = `
+exports[`error overlay (browser) keeps warnings out of the payload when the stats option does 1`] = `
 [
   "[webpack-dev-middleware] connected",
 ]
diff --git a/test/e2e/overlay.test.js b/test/e2e/overlay.test.js
index 433c5c1ac..37cb7f4cb 100644
--- a/test/e2e/overlay.test.js
+++ b/test/e2e/overlay.test.js
@@ -492,11 +492,11 @@ describe("error overlay (browser)", () => {
     expect(normalizeConsole(console_.messages)).toMatchSnapshot();
   });
 
-  it("keeps warnings out of the payload with hot.statsOptions", async () => {
+  it("keeps warnings out of the payload when the stats option does", async () => {
     hotApp = await createHotApp({
-      // The README's documented recipe: keep warnings in the build output
-      // but out of the SSE payload entirely.
-      hot: { statsOptions: { warnings: false } },
+      // One setting governs what a build reports in the terminal and in the
+      // browser; `hot.statsOptions` is deprecated and must not be used here.
+      stats: "errors-only",
       code: warningApp("v1"),
     });
     ({ page, browser } = await runBrowser());
@@ -1092,4 +1092,68 @@ describe("overlay shared state across bundled copies (browser)", () => {
       await page.evaluate(() => document.querySelectorAll("iframe").length),
     ).toBe(1);
   });
+
+  it("restyles a card that is already open", async () => {
+    await start();
+    await page.goto(hotApp.url);
+
+    await page.evaluate(() => {
+      globalThis.overlayA.showProblems("errors", ["styled"], "a");
+    });
+    await overlayFrame();
+
+    // Configuring while a card exists has to reach that card, not only the
+    // next one rendered.
+    await page.evaluate(() => {
+      globalThis.overlayA.default({
+        overlayStyles: { background: "rgb(1, 2, 3)" },
+      });
+    });
+
+    const frame = await overlayFrame();
+
+    expect(
+      await frame.evaluate(
+        (id) => document.getElementById(id).style.background,
+        CARD_ID,
+      ),
+    ).toBe("rgb(1, 2, 3)");
+  });
+
+  it("renders an empty problem without markup", async () => {
+    await start();
+    await page.goto(hotApp.url);
+
+    // An empty message still opens the overlay; the encoder has nothing to
+    // escape and must not fall over on it.
+    await page.evaluate(() => {
+      globalThis.overlayA.showProblems("errors", [""], "a");
+    });
+
+    const frame = await overlayFrame();
+
+    expect(await frame.evaluate(() => document.body.innerHTML)).toContain(
+      "ERROR",
+    );
+  });
+
+  it("dismisses on Escape pressed inside the overlay frame", async () => {
+    await start();
+    await page.goto(hotApp.url);
+
+    await page.evaluate(() => {
+      globalThis.overlayA.showProblems("errors", ["dismiss me"], "a");
+    });
+
+    const frame = await overlayFrame();
+
+    // Clicking inside the card moves focus into the frame, so the keydown
+    // lands on the frame's own listener rather than the host page's.
+    await clickInFrame(page, frame, `#${CARD_ID}`);
+    await page.keyboard.press("Escape");
+
+    await waitForNoOverlay(page);
+
+    expect(await page.$(`#${OVERLAY_ID}`)).toBeNull();
+  });
 });
diff --git a/test/helpers/hot-app.js b/test/helpers/hot-app.js
index 4837eddee..171be5799 100644
--- a/test/helpers/hot-app.js
+++ b/test/helpers/hot-app.js
@@ -112,7 +112,7 @@ function makeConfig(
  * app becomes a named compilation whose client connects with `?name=<name>`
  * and renders from `<name>.js`. `pageHeaders` are sent with the HTML page
  * (e.g. a Content-Security-Policy).
- * @param {{ query?: string, code?: string, files?: Record<string, string>, apps?: { name: string, code: string }[], hot?: EXPECTED_ANY, pageHeaders?: Record<string, string>, publicPath?: string, setup?: (server: EXPECTED_ANY) => void, hmrPlugin?: boolean }} options options
+ * @param {{ query?: string, code?: string, files?: Record<string, string>, apps?: { name: string, code: string }[], hot?: EXPECTED_ANY, stats?: EXPECTED_ANY, pageHeaders?: Record<string, string>, publicPath?: string, setup?: (server: EXPECTED_ANY) => void, hmrPlugin?: boolean }} options options
  * @returns {Promise<EXPECTED_ANY>} handles for the running app
  */
 async function createHotApp({
@@ -121,6 +121,7 @@ async function createHotApp({
   files = {},
   apps,
   hot = true,
+  stats,
   pageHeaders = {},
   publicPath = "/",
   setup,
@@ -188,7 +189,7 @@ async function createHotApp({
       }
     });
 
-    instance = middleware(compiler, { hot });
+    instance = middleware(compiler, { hot, stats });
 
     const app = express();