diff --git a/src/client/Sidebar.tsx b/src/client/Sidebar.tsx
index 5684db7..eddb857 100644
--- a/src/client/Sidebar.tsx
+++ b/src/client/Sidebar.tsx
@@ -43,6 +43,7 @@ import {
 import { IconPanelBottomOutline16, IconPanelRightOutline16 } from './icons.tsx'
 import { Workbench, type WorkbenchActions } from './split-pane.tsx'
 import { useNarrowViewport } from './breakpoints.ts'
+import { layoutPushSize } from './layout-push.ts'
 import { parseDesktopEnv } from './desktop-env.ts'
 import { getWcoSnapshot, subscribeWco } from './wco.ts'
 import { getShellPreset } from './shell-presets.ts'
@@ -804,12 +805,15 @@ export function Sidebar(props: { ctx: Context; store: SidebarStore }) {
       dragCommitted.current = true
       stopDragScheduling()
       const last = lastDragSize.current
-      const adoptedWidth = !narrow && state?.panelOpen === true
-        ? Math.min(last?.width ?? state?.width ?? 0, window.innerWidth)
-        : 0
-      const adoptedHeight = !narrow && state?.bottomOpen === true
-        ? Math.min(last?.height ?? state?.bottomHeight ?? 0, window.innerHeight)
-        : 0
+      const { width: adoptedWidth, height: adoptedHeight } = layoutPushSize({
+        narrow,
+        panelOpen: state?.panelOpen === true,
+        bottomOpen: state?.bottomOpen === true,
+        width: last?.width ?? state?.width ?? 0,
+        bottomHeight: last?.height ?? state?.bottomHeight ?? 0,
+        viewportWidth: window.innerWidth,
+        viewportHeight: window.innerHeight,
+      })
       applyDrag(adoptedWidth, adoptedHeight)
       draggingRef.current = false
       measureCenter()
@@ -826,12 +830,15 @@ export function Sidebar(props: { ctx: Context; store: SidebarStore }) {
   // On NARROW viewports the drawer FLOATS over the app shell — no push, the
   // conversation keeps the full width behind the drawer.
   useEffect(() => {
-    const width = !narrow && snapshot.state?.panelOpen === true
-      ? Math.min(snapshot.state.width, window.innerWidth)
-      : 0
-    const height = !narrow && snapshot.state?.bottomOpen === true
-      ? Math.min(snapshot.state.bottomHeight, window.innerHeight)
-      : 0
+    const { width, height } = layoutPushSize({
+      narrow,
+      panelOpen: snapshot.state?.panelOpen === true,
+      bottomOpen: snapshot.state?.bottomOpen === true,
+      width: snapshot.state?.width ?? 0,
+      bottomHeight: snapshot.state?.bottomHeight ?? 0,
+      viewportWidth: window.innerWidth,
+      viewportHeight: window.innerHeight,
+    })
     writeGeometry(width, height)
   }, [narrow, snapshot.state?.panelOpen, snapshot.state?.width, snapshot.state?.bottomOpen, snapshot.state?.bottomHeight])
   // Unmount must release the push (issue #31): when the boundary swaps the
diff --git a/src/client/layout-push.ts b/src/client/layout-push.ts
new file mode 100644
index 0000000..cf235d6
--- /dev/null
+++ b/src/client/layout-push.ts
@@ -0,0 +1,32 @@
+/**
+ * Size written to `--dsh-sidebar-width` / `--dsh-sidebar-height`.
+ * The conversation column (output + composer) must keep at least
+ * {@link PANEL_MIN} of the viewport after the bottom panel claims height.
+ */
+import { BOTTOM_MIN, PANEL_MIN } from './state.ts'
+
+export interface LayoutPushInput {
+  narrow: boolean
+  panelOpen: boolean
+  bottomOpen: boolean
+  width: number
+  bottomHeight: number
+  viewportWidth: number
+  viewportHeight: number
+}
+
+export interface LayoutPushSize {
+  width: number
+  height: number
+}
+
+/** Compute the live layout-push size. Narrow drawers float and push 0. */
+export function layoutPushSize(input: LayoutPushInput): LayoutPushSize {
+  if (input.narrow) return { width: 0, height: 0 }
+  const maxWidth = Math.max(PANEL_MIN, input.viewportWidth)
+  const maxHeight = Math.max(BOTTOM_MIN, input.viewportHeight - PANEL_MIN)
+  return {
+    width: input.panelOpen ? Math.min(Math.max(0, input.width), maxWidth) : 0,
+    height: input.bottomOpen ? Math.min(Math.max(0, input.bottomHeight), maxHeight) : 0,
+  }
+}
diff --git a/src/client/layout.css b/src/client/layout.css
index 333f9b0..e634d79 100644
--- a/src/client/layout.css
+++ b/src/client/layout.css
@@ -44,6 +44,14 @@
 #root [data-dsh-frame] > [data-pane="conversation"],
 #root :has(> [data-slot="conversation"]) {
   margin-bottom: var(--dsh-sidebar-height, 0px);
+  /* Grid/flex items default to min-height:auto. A long unbreakable token
+     (OAuth URL) then grows this column past the viewport and clips the
+     composer + left-rail Settings row. min-height:0 lets the cell shrink;
+     overflow:hidden keeps paint inside the cell; overflow-wrap wraps the
+     token so it cannot force the cell's intrinsic size. */
+  min-height: 0;
+  overflow: hidden;
+  overflow-wrap: anywhere;
   transition: margin-bottom var(--ds-transition-duration-slow) var(--ds-ease-in-out);
 }
 
diff --git a/tests/layout-css.spec.ts b/tests/layout-css.spec.ts
new file mode 100644
index 0000000..3b42b9a
--- /dev/null
+++ b/tests/layout-css.spec.ts
@@ -0,0 +1,22 @@
+/**
+ * layout.css must let the DSH conversation column shrink below its content
+ * size. Without min-height:0 a long unbreakable URL grows the grid item
+ * past the viewport and clips the composer.
+ */
+import { readFileSync } from 'node:fs'
+import { describe, expect, it } from 'vitest'
+
+const css = readFileSync('src/client/layout.css', 'utf8')
+
+describe('layout.css conversation column', () => {
+  it('targets the AppFrame center column', () => {
+    expect(css).toContain('[data-pane="conversation"]')
+    expect(css).toContain('[data-slot="conversation"]')
+  })
+
+  it('allows the center column to shrink and wrap long tokens', () => {
+    expect(css).toMatch(/min-height:\s*0/)
+    expect(css).toMatch(/overflow:\s*hidden/)
+    expect(css).toMatch(/overflow-wrap:\s*anywhere/)
+  })
+})
diff --git a/tests/layout-push.spec.ts b/tests/layout-push.spec.ts
new file mode 100644
index 0000000..35b3fa9
--- /dev/null
+++ b/tests/layout-push.spec.ts
@@ -0,0 +1,75 @@
+/**
+ * Layout-push size contract: the conversation column (output + composer)
+ * must keep at least PANEL_MIN of the viewport after the bottom panel
+ * claims its height. A stale persisted bottomHeight (or a cap at 100vh)
+ * used to crush the composer off-screen.
+ */
+import { describe, expect, it } from 'vitest'
+import { BOTTOM_MIN, PANEL_MIN } from '../src/client/state.ts'
+import { layoutPushSize } from '../src/client/layout-push.ts'
+
+describe('layoutPushSize', () => {
+  it('pushes nothing on a narrow drawer viewport', () => {
+    expect(layoutPushSize({
+      narrow: true,
+      panelOpen: true,
+      bottomOpen: true,
+      width: 400,
+      bottomHeight: 400,
+      viewportWidth: 390,
+      viewportHeight: 700,
+    })).toEqual({ width: 0, height: 0 })
+  })
+
+  it('pushes nothing when both panels are collapsed', () => {
+    expect(layoutPushSize({
+      narrow: false,
+      panelOpen: false,
+      bottomOpen: false,
+      width: 400,
+      bottomHeight: 400,
+      viewportWidth: 1280,
+      viewportHeight: 800,
+    })).toEqual({ width: 0, height: 0 })
+  })
+
+  it('caps an oversize bottom panel so the conversation keeps PANEL_MIN', () => {
+    const viewportHeight = 800
+    const size = layoutPushSize({
+      narrow: false,
+      panelOpen: false,
+      bottomOpen: true,
+      width: 0,
+      bottomHeight: 10_000,
+      viewportWidth: 1280,
+      viewportHeight,
+    })
+    expect(size.height).toBe(viewportHeight - PANEL_MIN)
+    expect(size.height).toBeGreaterThanOrEqual(BOTTOM_MIN)
+    expect(viewportHeight - size.height).toBeGreaterThanOrEqual(PANEL_MIN)
+  })
+
+  it('caps an oversize right panel at the viewport width', () => {
+    expect(layoutPushSize({
+      narrow: false,
+      panelOpen: true,
+      bottomOpen: false,
+      width: 10_000,
+      bottomHeight: 0,
+      viewportWidth: 1280,
+      viewportHeight: 800,
+    })).toEqual({ width: 1280, height: 0 })
+  })
+
+  it('passes through in-range open sizes', () => {
+    expect(layoutPushSize({
+      narrow: false,
+      panelOpen: true,
+      bottomOpen: true,
+      width: 400,
+      bottomHeight: 220,
+      viewportWidth: 1280,
+      viewportHeight: 800,
+    })).toEqual({ width: 400, height: 220 })
+  })
+})