diff --git a/e2e/map-renderer.test.ts b/e2e/map-renderer.test.ts
index fd44482..6e32e49 100644
--- a/e2e/map-renderer.test.ts
+++ b/e2e/map-renderer.test.ts
@@ -326,6 +326,59 @@ describeEngines((engine) => {
     expect(Date.now() - started).toBeLessThan(10_000);
   });
 
+  test("a hidden tab pauses the render timeout", async () => {
+    // A slow style rather than a hanging tile source: WebKit keeps a hung
+    // request's connection after the map is destroyed, and a second one would
+    // starve the tests that follow.
+    const result = await page.evaluate(async () => {
+      let state: DocumentVisibilityState = "visible";
+      Object.defineProperty(document, "visibilityState", {
+        configurable: true,
+        get: () => state,
+      });
+      const setVisibility = (next: DocumentVisibilityState) => {
+        state = next;
+        document.dispatchEvent(new Event("visibilitychange"));
+      };
+      const sleep = (ms: number) =>
+        new Promise((resolve) => setTimeout(resolve, ms));
+      try {
+        setVisibility("hidden");
+        let settled = false;
+        const creating = window.mapPrinter
+          .createMapRenderer({
+            style: "/fixtures/style-geojson.json?delay=6000",
+            pixelRatio: 1,
+            tileSize: { width: 256, height: 256 },
+            channels: 3,
+            renderTimeoutMs: 1_000,
+          })
+          .then(
+            (renderer) => {
+              renderer.destroy();
+              return "resolved";
+            },
+            (err: Error) => err.message,
+          )
+          .finally(() => (settled = true));
+        await sleep(2_000);
+        const settledWhileHidden = settled;
+        setVisibility("visible");
+        const t0 = performance.now();
+        const message = await creating;
+        return { settledWhileHidden, message, visibleMs: performance.now() - t0 };
+      } finally {
+        setVisibility("visible");
+        delete (document as { visibilityState?: unknown }).visibilityState;
+      }
+    });
+
+    expect(result.settledWhileHidden).toBe(false);
+    expect(result.message).toMatch(/did not finish rendering within 1000 ms/);
+    expect(result.visibleMs).toBeGreaterThanOrEqual(900);
+    expect(result.visibleMs).toBeLessThan(5_000);
+  });
+
   test("rejects when the style cannot be loaded", async () => {
     const v = fitBounds(VIEW_BBOX, 256, 256);
     const [tile] = tileGrid(v, TILE_SIZE);
diff --git a/src/lib/map-renderer/README.md b/src/lib/map-renderer/README.md
index 3504e13..68433a2 100644
--- a/src/lib/map-renderer/README.md
+++ b/src/lib/map-renderer/README.md
@@ -90,8 +90,10 @@ gets, because plenty of MapLibre errors leave a map that renders correctly:
   map rendering.
 
 A render that does not reach `idle` within `renderTimeoutMs` rejects with a
-timeout error that names the tile. `document.visibilityState === "hidden"`
-stalls MapLibre's render loop, so the message says so when the tab is hidden.
+timeout error that names the tile. Only time spent with the document visible
+counts: a hidden tab pauses `requestAnimationFrame` and with it MapLibre's
+render loop, so switching away mid-export pauses the export rather than
+failing it.
 
 ### `maxTileSize(pixelRatio)`
 
diff --git a/src/lib/map-renderer/index.ts b/src/lib/map-renderer/index.ts
index 210d514..71806fd 100644
--- a/src/lib/map-renderer/index.ts
+++ b/src/lib/map-renderer/index.ts
@@ -136,17 +136,16 @@ export async function createMapRenderer(
     const gl = requireWebGl2(canvas);
 
     await new Promise<void>((resolve, reject) => {
-      const timer = setTimeout(
-        () => fail(timeoutError("The style", renderTimeoutMs)),
-        renderTimeoutMs,
+      const clearTimer = foregroundTimeout(renderTimeoutMs, () =>
+        fail(timeoutError("The style", renderTimeoutMs)),
       );
       const fail = (error: Error) => {
-        clearTimeout(timer);
+        clearTimer();
         reject(error);
       };
       rejectPending = fail;
       map.once("style.load", () => {
-        clearTimeout(timer);
+        clearTimer();
         resolve();
       });
     });
@@ -194,15 +193,11 @@ export async function createMapRenderer(
             }
             resolve();
           };
-          const timer = setTimeout(
-            () =>
-              fail(
-                timeoutError(`Tile ${tile.col},${tile.row}`, renderTimeoutMs),
-              ),
-            renderTimeoutMs,
+          const clearTimer = foregroundTimeout(renderTimeoutMs, () =>
+            fail(timeoutError(`Tile ${tile.col},${tile.row}`, renderTimeoutMs)),
           );
           const finish = () => {
-            clearTimeout(timer);
+            clearTimer();
             map.off("idle", onIdle);
             rejectPending = undefined;
           };
@@ -280,11 +275,34 @@ function describeError(event: ErrorEvent & { sourceId?: string }): Error {
 }
 
 function timeoutError(what: string, ms: number): Error {
-  const hidden =
-    document.visibilityState === "hidden"
-      ? " (the tab is hidden, which pauses map rendering)"
-      : "";
-  return new Error(`${what} did not finish rendering within ${ms} ms${hidden}`);
+  return new Error(`${what} did not finish rendering within ${ms} ms`);
+}
+
+/** setTimeout that only counts time while the document is visible: MapLibre
+ *  renders from requestAnimationFrame, which a hidden tab pauses. */
+function foregroundTimeout(ms: number, onTimeout: () => void): () => void {
+  let remaining = ms;
+  let startedAt = 0;
+  let timer: ReturnType<typeof setTimeout> | undefined;
+  const resume = () => {
+    if (timer !== undefined) return;
+    startedAt = Date.now();
+    timer = setTimeout(onTimeout, remaining);
+  };
+  const pause = () => {
+    if (timer === undefined) return;
+    clearTimeout(timer);
+    timer = undefined;
+    remaining -= Date.now() - startedAt;
+  };
+  const onVisibility = () =>
+    document.visibilityState === "hidden" ? pause() : resume();
+  document.addEventListener("visibilitychange", onVisibility);
+  onVisibility();
+  return () => {
+    pause();
+    document.removeEventListener("visibilitychange", onVisibility);
+  };
 }
 
 function requireWebGl2(canvas: HTMLCanvasElement): WebGL2RenderingContext {