diff --git a/src/client/FreeWindow.tsx b/src/client/FreeWindow.tsx
index 4768741..6b37a6d 100644
--- a/src/client/FreeWindow.tsx
+++ b/src/client/FreeWindow.tsx
@@ -284,8 +284,12 @@ export function FreeWindow(props: {
           anchor={<span />}
         />
       </div>
+      {/* The tab cell reuses .paneTab (the pane's per-tab wrapper): the
+          column-flex chain (window → .floatContent → .paneTab) is what
+          gives the component a definite width via align-stretch — the exact
+          sizing contract a tab gets inside a pane. */}
       <div className={css.floatContent}>
-        {renderTab(float.tab, true, float.id)}
+        <div className={css.paneTab}>{renderTab(float.tab, true, float.id)}</div>
       </div>
       <div
         className={css.floatResize}
diff --git a/src/client/sidebar.module.css b/src/client/sidebar.module.css
index 38ec7cf..4b90cc6 100644
--- a/src/client/sidebar.module.css
+++ b/src/client/sidebar.module.css
@@ -361,11 +361,18 @@ body[data-dsh-sidebar-dragging] .bottomPanel {
   color: var(--dsw-alias-label-primary);
 }
 
+/* Mirrors .paneContent's column-flex contract: the tab cell must hand its
+   child a definite WIDTH via align-stretch. A row flex (the default) sizes
+   the main axis (width) from content — intrinsic-zero hosts (e.g. a plugin
+   tab UI) collapse to a 0px-wide sliver and paint nothing (the blank
+   whale-report window). */
 .floatContent {
   flex: 1;
   min-height: 0;
   min-width: 0;
   display: flex;
+  flex-direction: column;
+  overflow: hidden;
 }
 
 /* The SE resize corner (mirror of .cornerHandle). */
diff --git a/tests/e2e/float-window.e2e.ts b/tests/e2e/float-window.e2e.ts
index 303385f..52c5bb7 100644
--- a/tests/e2e/float-window.e2e.ts
+++ b/tests/e2e/float-window.e2e.ts
@@ -144,6 +144,18 @@ async function conversationBox(page: Page): Promise<{ x: number; y: number; widt
   })
 }
 
+/** The float's content cell must hand its child a real width (the
+ *  column-flex contract): a collapsed 0px cell paints nothing — the tab is
+ *  "in" the window but invisible. */
+async function assertContentPainted(page: Page, label: string): Promise<void> {
+  const width = await page.evaluate(() => {
+    const cell = document.querySelector('[data-dsh-float-window] [class*="floatContent"]')
+    const child = cell?.firstElementChild
+    return child === null || child === undefined ? -1 : Math.round(child.getBoundingClientRect().width)
+  })
+  expect(width, `${label}: the floated tab's content must have real width`).toBeGreaterThan(200)
+}
+
 test('float a tab, move the window, reload restores it, dock it back', async ({ page }) => {
   const sidebar = await bootExpanded(page)
 
@@ -158,6 +170,7 @@ test('float a tab, move the window, reload restores it, dock it back', async ({
   await expect(floatWindow).toHaveCount(1, { timeout: 10_000 })
   // The tab left the strip with the window born over the conversation area
   // (center), well clear of the panel's right edge.
+  await assertContentPainted(page, 'context-menu float')
   const leftBefore = await floatWindow.evaluate((node) => Number.parseFloat((node as HTMLElement).style.left))
   expect(Number.isFinite(leftBefore), `style.left must be numeric, got ${leftBefore}`).toBe(true)
   expect(leftBefore).toBeGreaterThan(0)
@@ -240,5 +253,6 @@ test('dragging a tab onto the conversation area floats it (drag-out gesture)', a
   // its title.
   await expect(stripTabs).toHaveCount(1)
   await expect(floatWindow.locator('[class*="floatTitle"]')).toHaveText(terminalTitle)
+  await assertContentPainted(page, 'drag-out float')
   await assertNoCrash(page)
 })