diff --git a/tools/e2e/13-frames.mjs b/tools/e2e/13-frames.mjs
index 2a6d03d7..75de3b46 100644
--- a/tools/e2e/13-frames.mjs
+++ b/tools/e2e/13-frames.mjs
@@ -1,4 +1,5 @@
 import { colourDistance } from '../lib/harness.mjs';
+import { openTab } from './lib/scaffold.mjs';
 
 /**
  * The Texture tab: cutting frames out of a sheet, and a sprite wearing one.
@@ -41,8 +42,8 @@ export async function frames(t) {
   await evaluate('__gm.state.select(null)');
   const texture = await json("(__gm.state.project.assets.find((a) => a.type === 'texture') ?? {}).id ?? ''");
   await evaluate(`__gm.state.select({ kind: 'asset', assetId: ${JSON.stringify(texture)} })`);
-  await clickText('Texture');
-  await sleep(600);
+  await openTab(t, 'texture');
+  await sleep(400);
   check('the Texture tab opens', (await json('__gm.tab()')) === 'texture');
   check(
     'and shows the selected sheet',
diff --git a/tools/e2e/14-overflow.mjs b/tools/e2e/14-overflow.mjs
index 6403c09d..9dd9e8ba 100644
--- a/tools/e2e/14-overflow.mjs
+++ b/tools/e2e/14-overflow.mjs
@@ -1,3 +1,5 @@
+import { TAB_LABELS } from './lib/scaffold.mjs';
+
 /**
  * Labels must be shortened to fit their control, not written past it. Runs last because it renames
  * assets to absurd lengths to provoke the case.
@@ -6,20 +8,6 @@
 /** A name far wider than any 200 px picker, so a control that does not truncate must spill. */
 const LONG_NAME = 'Player movement with jumping and coyote time';
 
-/** What the tab buttons read, to find one in the overflow menu. */
-const LABELS = {
-  scene: 'Scene',
-  game: 'Game',
-  graph: 'Behavior',
-  statemachine: 'State machine',
-  shader: 'Shader',
-  texture: 'Texture',
-  animation: 'Animation',
-  container: 'Container',
-  list: 'List',
-  particles: 'Particles',
-};
-
 export async function overflow(t) {
   const { check, sleep, json, evaluate, shot, mutate, drag, clickText } = t;
 
@@ -105,14 +93,14 @@ export async function overflow(t) {
   const offered = await json('__gm.overlayTexts()');
   check(
     'the overflow button offers every tab that had to go',
-    narrow.hidden.every((tab) => offered.includes(LABELS[tab])),
+    narrow.hidden.every((tab) => offered.includes(TAB_LABELS[tab])),
     JSON.stringify({ offered, hidden: narrow.hidden }),
   );
-  await clickText(LABELS[wanted]);
+  await clickText(TAB_LABELS[wanted]);
   await sleep(400);
   const picked = await json('__gm.tabRow()');
   check(
-    `picking ${LABELS[wanted]} from the overflow menu opens it and puts it in the row`,
+    `picking ${TAB_LABELS[wanted]} from the overflow menu opens it and puts it in the row`,
     (await json('__gm.tab()')) === wanted && picked.shown.some((b) => b.tab === wanted),
     JSON.stringify({ tab: await json('__gm.tab()'), shown: picked.shown.map((b) => b.tab) }),
   );
diff --git a/tools/e2e/16-container.mjs b/tools/e2e/16-container.mjs
index b89b9d74..4dded399 100644
--- a/tools/e2e/16-container.mjs
+++ b/tools/e2e/16-container.mjs
@@ -1,4 +1,5 @@
 import { instanceChild } from '../lib/builders.mjs';
+import { openTab } from './lib/scaffold.mjs';
 
 /**
  * The Container tab: editing a template with the scene view's tools. Relies on the container step
@@ -38,8 +39,8 @@ export async function containerTab(t) {
   await sleep(200);
 
   // 16a. The tab opens on the container the project has, and its header says which one.
-  await clickText('Container');
-  await sleep(500);
+  await openTab(t, 'container');
+  await sleep(300);
   const template = await json(`__gm.state.project.assets.find(a => a.id === '${containerId}').objects`);
   const count = template.length;
   check(
diff --git a/tools/e2e/25-animation.mjs b/tools/e2e/25-animation.mjs
index 3d41a63d..a221ab44 100644
--- a/tools/e2e/25-animation.mjs
+++ b/tools/e2e/25-animation.mjs
@@ -1,6 +1,6 @@
 import { colourDistance } from '../lib/harness.mjs';
 import { edge, node, propertiesOf, variable, written } from '../lib/builders.mjs';
-import { MAKE_OBJECT } from './lib/scaffold.mjs';
+import { MAKE_OBJECT, openTab } from './lib/scaffold.mjs';
 
 /**
  * Animations: made from a texture, edited in their own tab, worn by a sprite through `texture`,
@@ -132,8 +132,8 @@ export async function animation(t) {
 
   // 25c. The Animation tab shows it and plays it; the inspector keeps its two properties.
   await evaluate(`__gm.state.select({ kind: 'asset', assetId: ${JSON.stringify(walk.id)} })`);
-  await clickText('Animation');
-  await sleep(500);
+  await openTab(t, 'animation');
+  await sleep(300);
   check(
     'the inspector edits frames per second and playback',
     (await t.has('Frames per second')) && (await t.has('Playback')) && (await t.has('Loop')),
diff --git a/tools/e2e/lib/scaffold.mjs b/tools/e2e/lib/scaffold.mjs
index 8e3b3b2b..c367ed4f 100644
--- a/tools/e2e/lib/scaffold.mjs
+++ b/tools/e2e/lib/scaffold.mjs
@@ -100,3 +100,32 @@ export async function scaffoldBehavior(t, options) {
     },
   };
 }
+
+/** What each tab button reads – the text a check has to click to open it. */
+export const TAB_LABELS = {
+  scene: 'Scene',
+  game: 'Game',
+  graph: 'Behavior',
+  statemachine: 'State machine',
+  shader: 'Shader',
+  texture: 'Texture',
+  animation: 'Animation',
+  container: 'Container',
+  list: 'List',
+  particles: 'Particles',
+};
+
+/**
+ * Opens a tab by clicking it, through the `»` menu when the row had to hide it. Since the tenth tab
+ * (#73) that is the normal case at the test window's width: a plain `clickText('Container')` found
+ * nothing and took the whole suite down with it.
+ */
+export async function openTab(t, tab) {
+  const row = await t.json('__gm.tabRow()');
+  if (row.hidden.includes(tab)) {
+    await t.clickText('»');
+    await t.sleep(300);
+  }
+  await t.clickText(TAB_LABELS[tab]);
+  await t.sleep(400);
+}