diff --git a/e2e/specs/phone-search.spec.ts b/e2e/specs/phone-search.spec.ts
new file mode 100644
index 0000000..cdd7c9d
--- /dev/null
+++ b/e2e/specs/phone-search.spec.ts
@@ -0,0 +1,322 @@
+import { test, expect } from '../support/fixtures.js';
+
+/**
+ * #57. Below 600px the top bar is not in the layout, and search is a
+ * button that opens a modal on the pages where searching means
+ * anything.
+ *
+ * **This is the tier that can answer it, with one honest exception.**
+ * The shell's breakpoints are media queries, which the component tier
+ * cannot set — so whether the bar is a grid row, and whether a header
+ * grows a search button, is a question for a real viewport. What this
+ * tier *cannot* answer is the reason the surface is a `wa-dialog`:
+ * #60 read out of the Web Awesome source that `wa-popup` falls back to
+ * `position: fixed` where there is no Popover API (Chrome 113, the
+ * reference device) and that `.main-panel`'s `contain: paint` clips a
+ * fixed descendant. Chromium and WebKit here both have the Popover API,
+ * so a popup is top-layered and correct, and **an assertion that the
+ * modal is not clipped would pass on the broken build.** The mechanism
+ * is asserted in `frontend/test/components/search-dialog.test.ts`
+ * instead, where "is there a native <dialog>" is a question a browser
+ * can answer without lying.
+ *
+ * **And it is measured per element.** `layout-overflow.spec.ts` asks
+ * whether the *shell* needs sideways scrolling and was green throughout
+ * the defect it is named for; the win this issue is for is vertical and
+ * belongs to one element, so it is that element's box that is read.
+ */
+type Page = import('@playwright/test').Page;
+
+/** The reference device's own viewport, and a common small phone. */
+const DEVICE = { width: 424, height: 439 };
+const PHONE = { width: 390, height: 780 };
+
+/**
+ * Where the top bar is, and how much of the screen it costs.
+ *
+ * `contentTop` is measured against the *jobs band* rather than against
+ * the window, because that band is a real grid row whenever work is in
+ * flight (#62) and the app under these specs is long-lived — a job
+ * staged by another file is still in the store. Measuring against zero
+ * makes this assertion say "and no background job is running", which is
+ * not what it is for and is not something it can arrange.
+ */
+const barBox = (page: Page) =>
+  page.evaluate(() => {
+    const bar = document.querySelector<HTMLElement>('header.top-bar')!;
+    const main = document.querySelector<HTMLElement>('.main-panel')!;
+    const band = document.querySelector<HTMLElement>('job-band');
+    const cs = getComputedStyle(bar);
+
+    return {
+      position: cs.position,
+      height: Math.round(bar.getBoundingClientRect().height),
+      /** Where the content starts, and where the row above it ends. */
+      contentTop: Math.round(main.getBoundingClientRect().top),
+      aboveBottom: Math.round(band?.getBoundingClientRect().bottom ?? 0),
+    };
+  });
+
+test.describe('the phone has no top bar', () => {
+  test.beforeEach(async ({ app }) => {
+    await app.setViewportSize(DEVICE);
+  });
+
+  test.afterEach(async ({ app }) => {
+    await app.setViewportSize({ width: 1440, height: 900 });
+  });
+
+  /**
+   * The vertical win, measured rather than asserted by the absence of
+   * an element: `display: none` on the header would satisfy "the bar is
+   * hidden" while leaving a 3.25em grid row exactly where it was.
+   */
+  test('gives the row back to the content', async ({ app }) => {
+    const box = await barBox(app);
+
+    // Out of flow, so it takes no row — and 1px rather than 0, because
+    // it still carries the document's h1.
+    expect(box.position).toBe('absolute');
+    expect(box.height).toBeLessThanOrEqual(1);
+
+    // The content starts where the row above it ends, and there is no
+    // row above it but the jobs band. On `main` at the time of writing
+    // the content started 52px down from that point.
+    expect(box.contentTop).toBe(box.aboveBottom);
+  });
+
+  /**
+   * The wordmark yields its width and not its existence, which is the
+   * rule `top-bar-fit.ts` already lives by one band up: with the bar
+   * gone, `display: none` would take this document from one top-level
+   * heading to none on every page whose own header has no h1 —
+   * Settings has no `page-header` at all.
+   */
+  test('still has a top-level heading', async ({ app }) => {
+    await expect(
+      app.getByRole('heading', { name: 'YellowJacket', level: 1 }),
+    ).toHaveCount(1);
+  });
+
+  /**
+   * And its four controls are gone from the tab order, not merely from
+   * sight. A visually-hidden container is still focusable, and tabbing
+   * into a search box nobody can see is worse than not having one.
+   */
+  test('leaves nothing in the bar to tab into', async ({ app }) => {
+    for (const tag of [
+      'nav-history',
+      'library-filter',
+      'search-bar',
+      'job-indicator',
+    ]) {
+      await expect(app.locator(`header.top-bar ${tag}`)).toBeHidden();
+    }
+
+    const focusable = await app.evaluate(
+      () =>
+        document
+          .querySelector('header.top-bar')!
+          .querySelectorAll('input, select, button, a[href]').length,
+    );
+
+    // Nothing in the bar is *rendered*, so nothing in it can be
+    // focused; the controls are display:none, which takes their own
+    // shadow content with them.
+    expect(focusable).toBe(0);
+  });
+});
+
+test.describe('search on a phone', () => {
+  test.beforeEach(async ({ app }) => {
+    await app.setViewportSize(PHONE);
+  });
+
+  test.afterEach(async ({ app }) => {
+    await app.setViewportSize({ width: 1440, height: 900 });
+  });
+
+  test('is a button in the view that can be searched', async ({ app }) => {
+    await app.getByTestId('tab-tracks').click();
+    await expect(app.getByTestId('main-content')).toHaveAttribute(
+      'data-active-view',
+      'tracks',
+    );
+
+    // Scoped to the view: every cached primary view holds a
+    // `page-header`, and an unscoped testid is `bottom-nav`'s
+    // "resolved to 2 elements" trap again.
+    const trigger = app.locator('track-list page-header search-trigger button');
+
+    await expect(trigger).toBeVisible();
+    await expect(trigger).toHaveAttribute('aria-label', 'Search tracks');
+  });
+
+  /**
+   * The whole journey, which is the thing the issue asks for: a button,
+   * a modal, and the results on the page behind it saying what they are
+   * showing.
+   */
+  test('opens a modal, filters the page, and says so', async ({ app }) => {
+    await app.getByTestId('tab-tracks').click();
+    await expect(app.getByTestId('main-content')).toHaveAttribute(
+      'data-active-view',
+      'tracks',
+    );
+
+    await app.locator('track-list page-header search-trigger button').click();
+
+    const dialog = app.getByTestId('search-dialog');
+
+    // Attached, not visible: `wa-dialog`'s host is `display: contents`,
+    // so the element carrying the testid always reports hidden — what
+    // is visible is the native `<dialog>` inside it. That awkwardness
+    // is written down in CLAUDE.md and is why the assertion that this
+    // is really up is the role query below.
+    await expect(dialog).toBeAttached();
+
+    // Named, which `getByRole` can answer and the a11y snapshot cannot
+    // — the snapshot never prints a dialog's name, named or not. This
+    // is also the assertion that the dialog is genuinely showing.
+    await expect(
+      app.getByRole('dialog', { name: 'Search tracks' }),
+    ).toBeVisible();
+
+    // Scoped: the header's own box is still in the document, hidden.
+    // This is the one moment there are two `search-input`s.
+    await dialog.getByTestId('search-input').fill('aurora');
+
+    // Enter hands the screen back, because the results are the page.
+    await app.keyboard.press('Enter');
+    await expect(dialog).not.toBeAttached();
+
+    // Polled: the box debounces by 150ms, so reading the page once
+    // straight after closing the dialog can capture the state before
+    // the term ever reached the store.
+    await expect
+      .poll(() =>
+        app.evaluate(
+          () =>
+            document
+              .querySelector('[data-testid="main-content"] track-list')
+              ?.shadowRoot?.querySelector('page-header')
+              ?.shadowRoot?.querySelector('[data-testid="page-search-scope"]')
+              ?.textContent?.trim() ?? '',
+        ),
+      )
+      .toMatch(/matching.*aurora/);
+
+    // And the button says the search is on, in its name rather than
+    // only in its colour.
+    await expect(
+      app.locator('track-list page-header search-trigger button'),
+    ).toHaveAttribute('aria-label', /aurora/);
+
+    // Leave the app as the next spec expects to find it.
+    await app.locator('track-list page-header search-trigger button').click();
+    await app.getByTestId('search-dialog').getByTestId('search-input').fill('');
+    await app.keyboard.press('Escape');
+  });
+
+  /**
+   * Two of the seven searchable views have no `page-header` — they are
+   * detail views that filter on the term and say so in their own
+   * headers. A trigger placed only in `page-header` would leave them
+   * with a search they can show and no way to set it, which is #24's
+   * sentence broken in the band it was written for.
+   */
+  test('reaches the playlist detail view too', async ({ app }) => {
+    await app.getByTestId('tab-playlists').click();
+    await expect(app.getByTestId('main-content')).toHaveAttribute(
+      'data-active-view',
+      'playlists',
+    );
+
+    // `.playlist-item`, which is what the list renders. Asserted to
+    // exist rather than skipped on: the seed has a playlist, and a
+    // spec that quietly skips when its selector stops matching is a
+    // spec that reports success for a renamed class.
+    const first = app.locator('playlist-view .playlist-item').first();
+
+    await expect(first).toBeVisible();
+    await first.dblclick();
+
+    await expect(app.getByTestId('main-content')).toHaveAttribute(
+      'data-active-view',
+      'playlist-details',
+    );
+
+    await expect(
+      app.locator('playlist-details search-trigger button'),
+    ).toBeVisible();
+  });
+
+  /**
+   * A button that cannot do anything is worse than none — the rule
+   * `library-status-indicator` was rewritten on. Home has nothing of
+   * its own to search and is not in the store's map.
+   */
+  test('offers no button where there is nothing to search', async ({ app }) => {
+    await app.getByTestId('tab-home').click();
+    await expect(app.getByTestId('main-content')).toHaveAttribute(
+      'data-active-view',
+      'home',
+    );
+
+    await expect(
+      app.locator('home-view page-header search-trigger button'),
+    ).toHaveCount(0);
+  });
+
+  test('offers no button on a desktop, where the header has a box', async ({
+    app,
+  }) => {
+    await app.setViewportSize({ width: 1440, height: 900 });
+    await app.getByTestId('nav-tracks').click();
+
+    await expect(
+      app.locator('track-list page-header search-trigger button'),
+    ).toHaveCount(0);
+    await expect(app.locator('header.top-bar search-bar')).toBeVisible();
+  });
+});
+
+/**
+ * #148, which #57 inherits: `library-filter` is the only control in the
+ * app that calls `setSelectedLibrary`, and the bar it lived in is gone
+ * on a phone. #143 refused to hide it as a fit step for exactly this
+ * reason, so dropping it here would have been the same trade.
+ */
+test.describe('the library filter has a home that is not the bar', () => {
+  test.afterEach(async ({ app }) => {
+    await app.setViewportSize({ width: 1440, height: 900 });
+  });
+
+  test('is in Settings, and is reachable from a phone', async ({ app }) => {
+    await app.setViewportSize(PHONE);
+
+    await app.getByTestId('tab-more').click();
+    await app.getByTestId('nav-drawer').getByTestId('nav-settings').click();
+
+    await expect(app.getByTestId('main-content')).toHaveAttribute(
+      'data-active-view',
+      'settings',
+    );
+
+    const filter = app.getByTestId('settings-library-filter');
+
+    await expect(filter).toBeVisible();
+    await expect(filter.locator('select')).toBeVisible();
+  });
+
+  test('and it is the same control at every width', async ({ app }) => {
+    // Not a phone-only copy: "where do I change which library I am
+    // browsing" having two answers by viewport is the fault, not the
+    // fix.
+    await app.setViewportSize({ width: 1440, height: 900 });
+    await app.getByTestId('nav-settings').click();
+
+    await expect(app.getByTestId('settings-library-filter')).toBeVisible();
+    await expect(app.locator('header.top-bar library-filter')).toBeVisible();
+  });
+});
diff --git a/e2e/specs/top-bar-fit.spec.ts b/e2e/specs/top-bar-fit.spec.ts
index 8f8423f..badd8d0 100644
--- a/e2e/specs/top-bar-fit.spec.ts
+++ b/e2e/specs/top-bar-fit.spec.ts
@@ -26,10 +26,22 @@ type Page = import('@playwright/test').Page;
  * 600 is the bottom of the Compact band (#24) and where the defect
  * lands; 899 and 900 straddle `nav-history` appearing (68px more to
  * find, at the width that just gained the sidebar's labels); 800 is the
- * enforced minimum; 390 is a phone, where the answer must be that
- * nothing collapses because the media queries already did the work.
+ * enforced minimum.
+ *
+ * **390 is kept, and what it asks changed with #57.** There is no bar
+ * to fit below 600px any more — it is out of the grid and visually
+ * hidden — so "nothing hangs out of it" is a claim about an element
+ * with no row, and would pass on a build that had merely broken the
+ * bar. Dropping the width would be dropping the one place this file
+ * can still say something true about a phone, so it asserts the
+ * *stronger* property instead, below: the bar is out of the layout
+ * altogether, which is the thing #57 wanted and the thing that makes
+ * fitting moot.
  */
-const WIDTHS = [390, 600, 800, 899, 900, 1440];
+const WIDTHS = [600, 800, 899, 900, 1440];
+
+/** Where #57 leaves the bar, and where the desktop still has one. */
+const PHONE_WIDTH = 390;
 
 /**
  * A scan whose title is as long as a real one gets. The label is capped
@@ -90,6 +102,56 @@ const collapsed = (page: Page) =>
   }));
 
 test.describe('the top bar fits the window', () => {
+  /**
+   * The phone's answer, which is not "it fits" (#57).
+   *
+   * The bar has no grid row below 600px, so measuring its children
+   * against its content box is measuring a 1px box that is already
+   * invisible — a fit pass would collapse the wordmark every time and
+   * report success about nothing, which is why `measureTopBarFit`
+   * declines to run at all when the bar is out of flow. What is worth
+   * asserting here is that the fit pass has not quietly started
+   * *undoing* that: a rule that put the bar back in the layout would
+   * pass every assertion in this file and cost a 439px screen 12% of
+   * its height.
+   */
+  test(`the bar is out of the layout at ${PHONE_WIDTH}px, with a job running`, async ({
+    app,
+    testctl,
+  }) => {
+    await app.setViewportSize({ width: PHONE_WIDTH, height: 600 });
+    await testctl.emit('JobsChanged', [LONG_JOB]);
+
+    // Not merely hidden: `display: none` on the header would satisfy
+    // "invisible" and leave the 3.25em row exactly where it was. So
+    // the assertion is that the content starts where the row above it
+    // ends -- and with a job staged, the row above it is the jobs
+    // band, which is the whole reason this row could go.
+    await expect
+      .poll(() =>
+        app.evaluate(() => {
+          const bar = document.querySelector<HTMLElement>('header.top-bar')!;
+          const main = document.querySelector<HTMLElement>('.main-panel')!;
+          const band = document.querySelector<HTMLElement>('job-band')!;
+
+          return {
+            position: getComputedStyle(bar).position,
+            gap:
+              Math.round(main.getBoundingClientRect().top) -
+              Math.round(band.getBoundingClientRect().bottom),
+          };
+        }),
+      )
+      .toEqual({ position: 'absolute', gap: 0 });
+
+    // And the work is still visible, in the band that replaced the
+    // indicator (#62) — which is what made this row removable at all.
+    await expect(app.locator('job-indicator')).toBeHidden();
+    await expect(app.locator('job-band').locator('job-row')).toHaveCount(1);
+
+    await app.setViewportSize({ width: 1440, height: 900 });
+  });
+
   for (const width of WIDTHS) {
     test(`no control sits outside the bar at ${width}px, idle`, async ({
       app,
@@ -108,23 +170,7 @@ test.describe('the top bar fits the window', () => {
 
       // The indicator has to actually be up, or this test passes by
       // measuring the idle case under another name.
-      //
-      // Below 600px there is deliberately no indicator to measure:
-      // #62 stands it down and puts the rows in `<job-band>` instead,
-      // in the layout under the bar. So at 390 the assertion is that
-      // it *is* away and the bar still fits -- which is the same
-      // property (the bar has nothing hanging out of it) reached by the
-      // other branch of the same rule, rather than a width quietly
-      // dropped from the list.
-      const phone = width < 600;
-
-      await expect(app.locator('job-indicator'))[
-        phone ? 'toBeHidden' : 'toBeVisible'
-      ]();
-
-      if (phone) {
-        await expect(app.locator('job-band').locator('job-row')).toHaveCount(1);
-      }
+      await expect(app.locator('job-indicator')).toBeVisible();
 
       await expect.poll(() => overflowingChildren(app)).toEqual([]);
     });
diff --git a/frontend/index.css b/frontend/index.css
index 714699b..2875913 100644
--- a/frontend/index.css
+++ b/frontend/index.css
@@ -412,8 +412,17 @@ body div.sidebar {
    =================================================================== */
 @media (max-width: 599px) {
     body {
+        /* **There is no top-bar row here (#57).** Every one of the five
+           things that bar held has somewhere else to be below 600px:
+           `nav-history` is the platform's own gesture (gone from 899
+           down), the job indicator is `<job-band>` (#62), the search
+           box is a modal opened from the view's own header
+           (`search-trigger`), the library filter is Settings ->
+           Libraries (#148), and the wordmark is below. That is 3.25em
+           of a 439 CSS px viewport -- the single biggest vertical win
+           available on the reference device, which is why #57 asks for
+           the row rather than for a smaller bar. */
         grid-template:
-            "top-bar" 3.25em
             "jobs-band" auto
             "main-panel" 1fr
             "bottom-bar" auto
@@ -433,46 +442,55 @@ body div.sidebar {
         grid-area: bottom-nav;
     }
 
-    /* The 2em gutters are half a thumb each at this width, and the
-       subtitle is already gone from 900 down.
+    /* The bar is out of the layout, and out of it the way the *wordmark*
+       already goes at desktop widths: visually hidden rather than
+       `display: none`, because that `h1` is the document's top-level
+       heading and this app would otherwise have none on the pages whose
+       own header is empty by design (`page-header` renders no `h1` when
+       `heading` is '', and Settings has no `page-header` at all).
 
-       `min-width: 0` is the load-bearing half. A grid item's implicit
-       minimum is `auto` -- its content -- so a header whose children
-       ask for 580px makes the *body* 580px wide inside a 360px
-       viewport, and `overflow-x: hidden` then hides the right-hand
-       third of the app rather than fitting it. Every box between the
-       viewport and the content that must shrink needs this. */
+       Its four *controls* are `display: none` below, which is what
+       keeps them out of the tab order -- a visually-hidden container is
+       still focusable, and tabbing into a search box nobody can see is
+       worse than not having one.
+
+       This is `styles/sr-only.css.ts`'s recipe again, written out
+       because that one is a `CSSResult` for shadow roots and this is
+       the light DOM. `position: absolute` is also what tells
+       `services/top-bar-fit.ts` there is no row to fit into. */
     .top-bar {
-        padding-left: 0.75em;
-        padding-right: 0.75em;
-        gap: 0.5em;
-        min-width: 0;
+        position: absolute;
+        width: 1px;
+        height: 1px;
+        padding: 0;
+        margin: -1px;
         overflow: hidden;
+        clip-path: inset(50%);
+        white-space: nowrap;
+        border: 0;
+        gap: 0;
+        min-width: 0;
     }
 
+    .top-bar nav-history,
+    .top-bar library-filter,
+    .top-bar search-bar,
+    .top-bar job-indicator {
+        display: none;
+    }
+
+    /* `min-width: 0` is load-bearing wherever a box sits between the
+       viewport and content that must shrink. A grid item's implicit
+       minimum is `auto` -- its content -- so one child insisting on
+       580px makes the *body* 580px wide inside a 360px viewport, and
+       `overflow-x: hidden` then hides the right-hand third of the app
+       rather than fitting it. */
     .content-area,
     .main-panel,
     .bottom-bar {
         min-width: 0;
     }
 
-    .title {
-        font-size: 1.1em;
-    }
-
-    /* The search box is the one header control worth its width; the
-       library filter is a rarely-changed setting and reachable from
-       the drawer's Settings.
-
-       `nav-history` is already gone from 899 down. It would belong
-       here anyway and for a stronger reason than width: the phone has
-       Back as a gesture or a button the OS owns, and this app hooks it
-       (`popstate`), so a second Back in the chrome duplicates a
-       control the platform provides. */
-    .top-bar library-filter {
-        display: none;
-    }
-
     /* The full-screen now-playing view *is* the transport, so the bar
        repeating it underneath is 4em of a small screen spent saying
        the same thing twice -- visible in a screenshot, invisible to
@@ -486,11 +504,6 @@ body div.sidebar {
     body:has(#main-content[data-active-view="now-playing"]) .bottom-bar {
         display: none;
     }
-
-    .top-bar search-bar {
-        flex: 1 1 auto;
-        min-width: 0;
-    }
 }
 
 @media (max-width: 599px) {
@@ -543,16 +556,12 @@ body job-band {
    deletes this bar entirely and is blocked on the indicator having
    somewhere else to live -- this is that somewhere.
 
-   `display: none` rather than a fit step: `services/top-bar-fit.ts`
-   already skips children whose computed display is none, so the bar's
-   measurement simply sees one fewer child, and `[compact]` toggling on
-   a hidden element costs nothing. */
+   #57 has since done exactly that, so the indicator's own rule now
+   lives with the other three in the phone block above, where the bar
+   goes out of the layout in one statement rather than four. What stays
+   here is the band, and the argument for it.  */
 @media (max-width: 599px) {
-    .top-bar job-indicator {
-        display: none;
-    }
-
-    /* ...and its rows appear here, in the grid row above the content.
+    /* The indicator's rows appear here, in the grid row above the content.
        In flow rather than over it: a fixed band reads fine in a
        screenshot and is unusable, because at 424x439 a compact panel
        is ~200px of a 439px screen and it *covers* what is under it.
diff --git a/frontend/src/services/top-bar-fit.ts b/frontend/src/services/top-bar-fit.ts
index d253b46..24acaf9 100644
--- a/frontend/src/services/top-bar-fit.ts
+++ b/frontend/src/services/top-bar-fit.ts
@@ -119,6 +119,16 @@ export const FIT_STEPS: readonly FitStep[] = [
  * @returns the ids collapsed, in the order they were given up.
  */
 export function measureTopBarFit(bar: HTMLElement): string[] {
+    // Below 600px there is no bar to fit (#57): `index.css` takes it
+    // out of the grid and leaves it visually hidden at 1px, carrying
+    // nothing but the document's `h1`. Measuring that reports the
+    // wordmark as overflowing 1px of content box and collapses it every
+    // time -- true, and about nothing, since the whole bar is already
+    // invisible. Asking the *computed position* rather than the
+    // viewport width is what keeps this file free of a breakpoint the
+    // stylesheet already owns.
+    if (getComputedStyle(bar).position === 'absolute') return [];
+
     const fits = () => {
         const style = getComputedStyle(bar);
         const box = bar.getBoundingClientRect();