diff --git a/e2e/coach-answer-layout.spec.ts b/e2e/coach-answer-layout.spec.ts
index 0bf0979ee..fe13504f9 100644
--- a/e2e/coach-answer-layout.spec.ts
+++ b/e2e/coach-answer-layout.spec.ts
@@ -16,8 +16,8 @@ import { aiBlockAvailable, serveAiBlock } from "./setup/ai-capabilities";
  *      bubble's left edge and no taller than one 44 px target: copy, read
  *      aloud, try again, details, then the time. The model and the tokens
  *      are not text on the row; the details icon shows them in a tooltip on
- *      keyboard focus (desktop) and on a tap (phone), and a second tap or
- *      Escape closes it.
+ *      keyboard focus (desktop) and on a tap (phone); Enter and Space keep it
+ *      open, and a second tap or Escape closes it.
  *   2. The follow-up chips sit in the answer's column: their left edge is
  *      the bubble's, their text is the answer's size, and a chip is at most
  *      36 px tall beside a pointer and at least 44 px on a phone.
@@ -296,8 +296,14 @@ test.describe("Coach answer layout", () => {
     await expect(tip).toContainText("1,234 tokens");
     await expect(info).toHaveAttribute("aria-describedby", /.+/);
     await shoot(page, testInfo, `answer-info-${viewport.label}`);
-    if (desktop) await page.keyboard.press("Escape");
-    else await info.tap();
+    if (desktop) {
+      // Enter and Space on the focused icon keep it open; Escape closes it.
+      for (const key of ["Enter", "Space"]) {
+        await page.keyboard.press(key);
+        await expect(tip).toBeVisible();
+      }
+      await page.keyboard.press("Escape");
+    } else await info.tap();
     await expect(tip).toHaveCount(0);
 
     // 2. The chips in the answer's column, at the answer's size.
diff --git a/src/components/insights/coach-panel/__tests__/message-actions.test.tsx b/src/components/insights/coach-panel/__tests__/message-actions.test.tsx
index 45c326508..928dee229 100644
--- a/src/components/insights/coach-panel/__tests__/message-actions.test.tsx
+++ b/src/components/insights/coach-panel/__tests__/message-actions.test.tsx
@@ -50,7 +50,11 @@ vi.mock("../read-aloud", async (importOriginal) => {
 });
 
 import { ChatBubble, areChatBubblePropsEqual } from "../chat-bubble";
-import { answerInfoLines, messageTimeText } from "../message-actions";
+import {
+  answerInfoLines,
+  answerInfoOpenAfterClick,
+  messageTimeText,
+} from "../message-actions";
 
 function render(node: React.ReactNode, locale: "en" | "de" = "en") {
   return renderToStaticMarkup(
@@ -302,3 +306,15 @@ describe("answerInfoLines", () => {
     ]);
   });
 });
+
+describe("answerInfoOpenAfterClick", () => {
+  it("opens on Enter or Space, never closes, though focus opened it already", () => {
+    // A keyboard activation fires no pointer-down.
+    expect(answerInfoOpenAfterClick(null)).toBe(true);
+  });
+
+  it("toggles on a tap or a click from the state at pointer-down", () => {
+    expect(answerInfoOpenAfterClick(false)).toBe(true);
+    expect(answerInfoOpenAfterClick(true)).toBe(false);
+  });
+});
diff --git a/src/components/insights/coach-panel/message-actions.tsx b/src/components/insights/coach-panel/message-actions.tsx
index 773e2b5df..5748241af 100644
--- a/src/components/insights/coach-panel/message-actions.tsx
+++ b/src/components/insights/coach-panel/message-actions.tsx
@@ -180,15 +180,28 @@ function TryAgainButton({ onRegenerate }: { onRegenerate: () => void }) {
   );
 }
 
+/**
+ * Whether the details tooltip is open after a click on its icon, given its
+ * state when the pointer went down (`null`: no pointer went down, so Enter
+ * or Space activated the button). A tap or a mouse click toggles from that
+ * state, before the primitive's own pointer-down close ran. A keyboard
+ * activation always opens: focus has already opened the tooltip, and a
+ * toggle would close it on Enter. Escape is the keyboard's way out.
+ */
+export function answerInfoOpenAfterClick(
+  openAtPointerDown: boolean | null,
+): boolean {
+  return openAtPointerDown === null ? true : !openAtPointerDown;
+}
+
 /**
  * The model and token count of an answer, behind an info icon. A tooltip,
  * opened the three ways a reader can reach it: hovering the icon, focusing
  * it from the keyboard, and tapping it on a touch screen, where there is no
  * hover. A second tap, a tap elsewhere or Escape closes it.
  *
- * The tap is handled here because the tooltip primitive closes on every
- * click: the click toggles from the state the tooltip had when the pointer
- * went down, before the primitive's own pointer-down close ran.
+ * The click is handled here because the tooltip primitive closes on every
+ * click (`answerInfoOpenAfterClick` decides instead).
  */
 function AnswerInfoButton({ lines }: { lines: string[] }) {
   const { t } = useTranslations();
@@ -210,9 +223,8 @@ function AnswerInfoButton({ lines }: { lines: string[] }) {
             onClick={(event) => {
               // Keep the primitive from closing it again on this click.
               event.preventDefault();
-              const was = openAtPointerDown.current;
+              setOpen(answerInfoOpenAfterClick(openAtPointerDown.current));
               openAtPointerDown.current = null;
-              setOpen(was === null ? (current) => !current : !was);
             }}
           >
             <Info className="size-4" aria-hidden="true" />