diff --git a/src/web/public/tile-grid.js b/src/web/public/tile-grid.js
index 84bfc7c8..73b7a1e6 100644
--- a/src/web/public/tile-grid.js
+++ b/src/web/public/tile-grid.js
@@ -375,10 +375,8 @@ Object.assign(CodemanApp.prototype, {
    * replaces its set.
    */
   openTilePicker(event) {
-    // As the split picker: the opening event must not reach the outside-click
-    // listener this call installs.
+    // The right-click: the browser's own context menu stays away.
     event?.preventDefault?.();
-    event?.stopPropagation?.();
     if (this._tilePicker) {
       this.closeTilePicker();
       return;
@@ -472,18 +470,17 @@ Object.assign(CodemanApp.prototype, {
       menu.style.top = `${rect.bottom + 4}px`;
       menu.style.right = `${window.innerWidth - rect.right}px`;
     }
+    // A click elsewhere or Escape closes it. A click on the Tiles button needs no
+    // exception: its own handler (toggleTileGrid) closes the picker first.
     const onOutside = (e) => {
-      if (menu.contains?.(e.target) || e.target?.closest?.('.btn-tile-grid')) return;
+      if (menu.contains?.(e.target)) return;
       this.closeTilePicker();
     };
     const onKey = (e) => {
       if (e.key === 'Escape') this.closeTilePicker();
     };
     this._tilePicker = { menu, onOutside, onKey };
-    // Deferred a tick so the opening click (still bubbling) does not close it.
-    setTimeout(() => {
-      if (this._tilePicker?.menu === menu) document.addEventListener('click', onOutside);
-    }, 0);
+    document.addEventListener('click', onOutside);
     document.addEventListener('keydown', onKey);
     (boxes.find((b) => !b.disabled) || open).focus?.();
   },
diff --git a/test/tile-grid-open-set.test.ts b/test/tile-grid-open-set.test.ts
index f44769df..de4775dc 100644
--- a/test/tile-grid-open-set.test.ts
+++ b/test/tile-grid-open-set.test.ts
@@ -18,7 +18,14 @@ import { readFileSync } from 'node:fs';
 import { resolve } from 'node:path';
 import vm from 'node:vm';
 import { beforeEach, describe, expect, it, vi } from 'vitest';
-import { FakeEl, body, bySelector, makeGridApp, resetGridHarness } from './mocks/tile-grid-vm.js';
+import {
+  FakeEl,
+  body,
+  bySelector,
+  documentAddEventListener,
+  makeGridApp,
+  resetGridHarness,
+} from './mocks/tile-grid-vm.js';
 
 type OpenSet = { source: string; ids: string[]; focusedId: string | null } | null;
 type Helpers = { tileGridOpenSet(p: Record<string, unknown>): OpenSet; TILE_GRID_MAX: number };
@@ -137,6 +144,18 @@ describe('opening at once, in the app', () => {
     expect(app._tilesOwnTerminal()).toBe(true);
   });
 
+  it('a click elsewhere closes the picker; a click inside it does not', () => {
+    const app = makeGridApp(IDS);
+    const before = documentAddEventListener.mock.calls.length;
+    app.openTilePicker({ preventDefault: vi.fn() });
+    const calls = documentAddEventListener.mock.calls.slice(before) as Array<[string, (e: unknown) => void]>;
+    const onClick = calls.find(([type]) => type === 'click')![1];
+    onClick({ target: picker()!.children[0] });
+    expect(picker()).not.toBeNull();
+    onClick({ target: new FakeEl() });
+    expect(picker()).toBeNull();
+  });
+
   it('a right-click opens the picker and keeps the browser menu away', () => {
     const app = makeGridApp(IDS);
     const ev = { preventDefault: vi.fn(), stopPropagation: vi.fn() };