diff --git a/apps/web/src/__tests__/datahub-table-controls.test.tsx b/apps/web/src/__tests__/datahub-table-controls.test.tsx
new file mode 100644
index 000000000..5f96647d4
--- /dev/null
+++ b/apps/web/src/__tests__/datahub-table-controls.test.tsx
@@ -0,0 +1,40 @@
+import { cleanup, render, screen } from '@testing-library/react';
+import { afterEach, beforeEach, describe, expect, it, vi } from 'vitest';
+
+import { Route } from '@/routes/_app/datahub/index';
+
+import '@/services/i18n';
+
+vi.mock('@tanstack/react-router', async (importOriginal) => ({
+  ...(await importOriginal<typeof import('@tanstack/react-router')>()),
+  useNavigate: () => vi.fn()
+}));
+vi.mock('@/hooks/useSubjectsQuery', () => ({
+  subjectsQueryOptions: vi.fn(),
+  useSubjectsQuery: () => ({ data: [] })
+}));
+vi.mock('@/store', () => ({
+  useAppStore: (selector: (store: { currentGroup: null; currentUser: null }) => unknown) =>
+    selector({ currentGroup: null, currentUser: null })
+}));
+
+describe('data hub table controls', () => {
+  beforeEach(() => {
+    // The toggles call `Route.useNavigate()`, which warns outside a RouterProvider; no navigation happens here.
+    vi.spyOn(console, 'warn').mockImplementation(() => undefined);
+  });
+
+  afterEach(() => {
+    cleanup();
+    vi.restoreAllMocks();
+  });
+
+  // happy-dom computes no layout, so the wrapping is asserted through its utility classes;
+  // testing/src/specs/datahub.spec.ts measures the rendered result at phone width.
+  it('should let the controls wrap below the md breakpoint, so a phone never pushes Export off screen', () => {
+    const Component = Route.options.component!;
+    render(<Component />);
+    const controls = screen.getByTestId('subject-lookup-search-button').parentElement!;
+    expect([...controls.classList]).toEqual(expect.arrayContaining(['flex-wrap', 'md:flex-nowrap']));
+  });
+});
diff --git a/apps/web/src/components/InstrumentShowcase/InstrumentShowcase.tsx b/apps/web/src/components/InstrumentShowcase/InstrumentShowcase.tsx
index 5e24adc2a..df5ce225b 100644
--- a/apps/web/src/components/InstrumentShowcase/InstrumentShowcase.tsx
+++ b/apps/web/src/components/InstrumentShowcase/InstrumentShowcase.tsx
@@ -99,18 +99,18 @@ export const InstrumentShowcase: React.FC<{
       tabIndex={0}
       onKeyDown={handleKeyDown}
     >
-      <div className="flex items-center gap-2.5">
+      <div className="flex flex-col gap-2.5 lg:flex-row lg:items-center">
         <SearchBar
-          className="grow"
+          className="w-full grow"
           data-testid="instrument-search-bar"
           value={searchTerm}
           onValueChange={setSearchTerm}
         />
-        <div className="flex items-center gap-2.5">
-          <div data-testid="instrument-kind-filter">
+        <div className="flex w-full items-center gap-2.5 lg:w-auto">
+          <div className="grow lg:grow-0" data-testid="instrument-kind-filter">
             <InstrumentKindDropdown selected={selectedKinds} setSelected={setSelectedKinds} />
           </div>
-          <div data-testid="instrument-tag-filter">
+          <div className="grow lg:grow-0" data-testid="instrument-tag-filter">
             <ListboxDropdown
               widthFull
               options={tagOptions}
@@ -119,7 +119,7 @@ export const InstrumentShowcase: React.FC<{
               title={t('core.tags')}
             />
           </div>
-          <div data-testid="instrument-language-filter">
+          <div className="grow lg:grow-0" data-testid="instrument-language-filter">
             <InstrumentLanguageDropdown selected={selectedLanguages} setSelected={setSelectedLanguages} />
           </div>
         </div>
diff --git a/apps/web/src/components/InstrumentShowcase/__tests__/InstrumentShowcase.test.tsx b/apps/web/src/components/InstrumentShowcase/__tests__/InstrumentShowcase.test.tsx
index 794169635..7d3a9d759 100644
--- a/apps/web/src/components/InstrumentShowcase/__tests__/InstrumentShowcase.test.tsx
+++ b/apps/web/src/components/InstrumentShowcase/__tests__/InstrumentShowcase.test.tsx
@@ -17,6 +17,15 @@ describe('InstrumentShowcase', () => {
     expect(fireEvent.keyDown(searchBar, { key: 'Enter' })).toBe(false);
   });
 
+  // happy-dom computes no layout, so the responsive stacking is asserted through its utility classes;
+  // testing/src/specs/accessible-instruments.spec.ts measures the rendered result at phone width.
+  it('should stack the search bar above the filters below the lg breakpoint, so a phone gives it the full width', () => {
+    render(<InstrumentShowcase data={[]} onSelect={vi.fn()} />);
+    const searchBar = screen.getByTestId('instrument-search-bar');
+    expect([...searchBar.classList]).toContain('w-full');
+    expect([...searchBar.parentElement!.classList]).toEqual(expect.arrayContaining(['flex-col', 'lg:flex-row']));
+  });
+
   it('should not select anything when Enter is pressed with no matching instruments', () => {
     const onSelect = vi.fn();
     render(<InstrumentShowcase data={[]} onSelect={onSelect} />);
diff --git a/apps/web/src/routes/_app/datahub/index.tsx b/apps/web/src/routes/_app/datahub/index.tsx
index 4b2b785c1..186af5d93 100644
--- a/apps/web/src/routes/_app/datahub/index.tsx
+++ b/apps/web/src/routes/_app/datahub/index.tsx
@@ -61,7 +61,7 @@ const Filters: React.FC<{
     <DropdownMenu open={isOpen} onOpenChange={setIsOpen}>
       <DropdownMenu.Trigger asChild>
         <Button
-          className="flex items-center justify-between gap-2"
+          className="flex grow items-center justify-between gap-2 md:grow-0"
           data-testid="datahub-filters-trigger"
           variant="outline"
         >
@@ -300,11 +300,11 @@ const Toggles: React.FC<{
   };
 
   return (
-    <div className="flex gap-3">
+    <div className="flex flex-wrap gap-3 md:flex-nowrap">
       <Dialog open={isLookupOpen} onOpenChange={setIsLookupOpen}>
         <Dialog.Trigger asChild>
           <Button
-            className="gap-2"
+            className="grow gap-2 md:grow-0"
             data-spotlight-type="subject-lookup-search-button"
             data-testid="subject-lookup-search-button"
             id="subject-lookup-search-button"
diff --git a/testing/src/pages/_app/datahub/index.page.ts b/testing/src/pages/_app/datahub/index.page.ts
index e8e688c6d..59e05b930 100644
--- a/testing/src/pages/_app/datahub/index.page.ts
+++ b/testing/src/pages/_app/datahub/index.page.ts
@@ -9,7 +9,9 @@ export class DatahubPage extends AppPage {
   readonly pageHeader: Locator;
   readonly rowActionsTrigger: Locator;
   readonly rows: Locator;
+  readonly searchBar: Locator;
   readonly searchInput: Locator;
+  readonly subjectLookupButton: Locator;
   constructor(page: Page) {
     super(page);
     this.exportDropdown = page.getByTestId('datahub-export-dropdown');
@@ -18,7 +20,9 @@ export class DatahubPage extends AppPage {
     this.pageHeader = page.getByTestId('page-header');
     this.rowActionsTrigger = page.getByTestId('row-actions-trigger').first();
     this.rows = page.getByTestId('data-table-body').getByTestId('data-table-row');
-    this.searchInput = page.getByTestId('data-table-search-bar').getByRole('searchbox');
+    this.searchBar = page.getByTestId('data-table-search-bar');
+    this.searchInput = this.searchBar.getByRole('searchbox');
+    this.subjectLookupButton = page.getByTestId('subject-lookup-search-button');
   }
 
   /**
diff --git a/testing/src/pages/_app/instruments/accessible-instruments.page.ts b/testing/src/pages/_app/instruments/accessible-instruments.page.ts
index 6e42fd792..3e7fa657f 100644
--- a/testing/src/pages/_app/instruments/accessible-instruments.page.ts
+++ b/testing/src/pages/_app/instruments/accessible-instruments.page.ts
@@ -4,14 +4,18 @@ import { AppPage } from '../route.page';
 
 export class AccessibleInstrumentsPage extends AppPage {
   readonly instrumentShowcase: Locator;
+  readonly kindFilter: Locator;
   readonly pageHeader: Locator;
+  readonly searchBar: Locator;
   readonly searchBox: Locator;
 
   constructor(page: Page) {
     super(page);
     this.pageHeader = page.getByTestId('page-header');
     this.instrumentShowcase = page.getByTestId('instrument-showcase');
-    this.searchBox = page.getByTestId('instrument-search-bar').locator('input');
+    this.kindFilter = page.getByTestId('instrument-kind-filter');
+    this.searchBar = page.getByTestId('instrument-search-bar');
+    this.searchBox = this.searchBar.locator('input');
   }
 
   /** Cards carry a content-hash testid, so match on the visible title instead. */
diff --git a/testing/src/specs/accessible-instruments.spec.ts b/testing/src/specs/accessible-instruments.spec.ts
index 39470d695..a269ddb14 100644
--- a/testing/src/specs/accessible-instruments.spec.ts
+++ b/testing/src/specs/accessible-instruments.spec.ts
@@ -1,5 +1,24 @@
+import { PHONE_VIEWPORT } from '../support/constants';
 import { expect, test } from '../support/fixtures';
 
+test.describe('accessible instruments on a phone', () => {
+  test.use({ viewport: PHONE_VIEWPORT });
+
+  test('should give the search bar a full-width row above the filters, so the dropdowns cannot crowd it out', async ({
+    getPageModel
+  }) => {
+    const accessibleInstrumentsPage = await getPageModel('/instruments/accessible-instruments');
+    await expect(accessibleInstrumentsPage.searchBar).toBeVisible();
+
+    const showcaseBox = (await accessibleInstrumentsPage.instrumentShowcase.boundingBox())!;
+    const searchBarBox = (await accessibleInstrumentsPage.searchBar.boundingBox())!;
+    const kindFilterBox = (await accessibleInstrumentsPage.kindFilter.boundingBox())!;
+
+    expect(searchBarBox.width).toBeCloseTo(showcaseBox.width, 0);
+    expect(kindFilterBox.y).toBeGreaterThanOrEqual(searchBarBox.y + searchBarBox.height);
+  });
+});
+
 test.describe('accessible instruments', () => {
   test('should filter the instrument showcase to cards matching the search query', async ({ getPageModel }) => {
     const accessibleInstrumentsPage = await getPageModel('/instruments/accessible-instruments');
diff --git a/testing/src/specs/datahub.spec.ts b/testing/src/specs/datahub.spec.ts
index 3deb89fe3..e25a07795 100644
--- a/testing/src/specs/datahub.spec.ts
+++ b/testing/src/specs/datahub.spec.ts
@@ -1,9 +1,26 @@
 import { readFile } from 'node:fs/promises';
 
 import { DatahubPage } from '../pages/_app/datahub/index.page';
-import { HAPPINESS_RECORD } from '../support/constants';
+import { HAPPINESS_RECORD, PHONE_VIEWPORT } from '../support/constants';
 import { expect, test } from '../support/fixtures';
 
+test.describe('data hub on a phone', () => {
+  test.use({ viewport: PHONE_VIEWPORT });
+
+  test('should keep every table control within the width of the search bar, so none is pushed off screen', async ({
+    getPageModel
+  }) => {
+    const datahubPage = await getPageModel('/datahub');
+    await expect(datahubPage.exportDropdown).toBeVisible();
+
+    const searchBarBox = (await datahubPage.searchBar.boundingBox())!;
+    for (const control of [datahubPage.subjectLookupButton, datahubPage.filtersTrigger, datahubPage.exportDropdown]) {
+      const controlBox = (await control.boundingBox())!;
+      expect(controlBox.x + controlBox.width).toBeLessThanOrEqual(searchBarBox.x + searchBarBox.width);
+    }
+  });
+});
+
 test.describe('data hub', () => {
   test("should export the records of a group manager's own group, since the export applies the caller's read rules", async ({
     api,
diff --git a/testing/src/support/constants.ts b/testing/src/support/constants.ts
index cfd4a641e..4bfa926fa 100644
--- a/testing/src/support/constants.ts
+++ b/testing/src/support/constants.ts
@@ -41,3 +41,6 @@ export const E2E_MAIL_CONFIG = {
   senderName: 'Open Data Capture',
   username: 'e2e'
 } as const;
+
+/** A typical phone screen, narrower than the `md` breakpoint at which `apps/web` switches to its desktop layout. */
+export const PHONE_VIEWPORT = { height: 844, width: 390 } as const;