diff --git a/tests/browser/lobby.test.js b/tests/browser/lobby.test.js
index 2f82c9e6..9c4bc31d 100644
--- a/tests/browser/lobby.test.js
+++ b/tests/browser/lobby.test.js
@@ -1050,20 +1050,84 @@ lobbyTest(
 );
 
 lobbyTest(
-  "changing difficulty clears the previous random-pick exclusion",
+  "a drawn problem survives a difficulty change that still includes it",
   async (page) => {
     await page.addInitScript(() => {
       Math.random = () => 0;
     });
-    const before = await lobby(page);
+    await lobby(page);
     await page.click("#random-problem");
-    assert.notEqual((await snapshot(page)).card, before.card);
-    await setLevel(page, "Hard", true);
-    await setLevel(page, "Hard", false);
-    assert.equal((await snapshot(page)).card, before.card);
+    const drawn = await snapshot(page);
+    const level = (await cardInfo(page, drawn.card)).level;
+
+    const others = ["Easy", "Medium", "Hard"].filter((name) => name !== level);
+    for (const other of others) {
+      await setLevel(page, other, true);
+      assert.equal(
+        (await snapshot(page)).card,
+        drawn.card,
+        `checking ${other} redrew a problem it did not hide`,
+      );
+    }
+    // Returning from the media preflight re-runs the recommendation, and the
+    // roll that drew this problem names a different one under the new filter.
+    await restore(page);
+    await awaitReady(page);
+    assert.equal(
+      (await snapshot(page)).card,
+      drawn.card,
+      "a kept problem moved when the page was restored",
+    );
+    await setLevel(page, others[0], false);
+    assert.equal(
+      (await snapshot(page)).card,
+      drawn.card,
+      `unchecking ${others[0]} redrew a problem it did not hide`,
+    );
+
+    await setLevel(page, level, false);
+    const redrawn = await snapshot(page);
+    assert.notEqual(redrawn.card, drawn.card, "a hidden problem stayed picked");
+    const info = await cardInfo(page, redrawn.card);
+    assert.equal(info.level, others[1]);
+    assert.equal(info.hidden, false);
   },
 );
 
+// Widening the filter keeps the card on screen, but it was drawn from the
+// reports in hand, so refreshed ones that pass it decide again. The usual order
+// widens before leaving for the interview; the other widens inside the reload,
+// while the reports in hand still belong to the page before the candidate left.
+for (const [when, widenFirst] of [
+  ["before the interview", true],
+  ["while the history reloads", false],
+]) {
+  lobbyTest(
+    `a drawn problem kept ${when} is redrawn from the history it comes back to`,
+    async (page) => {
+      const shown = (await lobby(page)).card;
+      const widen = async () => {
+        await setLevel(page, "Hard", true);
+        assert.equal((await snapshot(page)).card, shown);
+      };
+
+      if (widenFirst) await widen();
+      const release = holdHistory();
+      reports = [hired(shown)];
+      await restore(page);
+      if (!widenFirst) await widen();
+
+      release();
+      await awaitReady(page);
+      assert.notEqual(
+        (await snapshot(page)).card,
+        shown,
+        "a problem the refreshed history passed stayed recommended",
+      );
+    },
+  );
+}
+
 lobbyTest(
   "Random problem waits for history on load and browser restore",
   async (page) => {
diff --git a/web/app.js b/web/app.js
index 7a90d634..49adca21 100644
--- a/web/app.js
+++ b/web/app.js
@@ -35,6 +35,11 @@ let reports = [];
 /// The practice focus the share box currently refers to.
 let sharedFocus = null;
 let manualProblem = false;
+/// The reports a drawn problem kept across a difficulty change was drawn from,
+/// serialized, or null when nothing is kept. Not `manualProblem`: a hand pick
+/// stands for good, while a kept draw stands only until the history it was
+/// drawn from changes.
+let keptDraw = null;
 let manualDuration = false;
 let manualDifficulty = false;
 let historyReady = false;
@@ -176,6 +181,7 @@ for (const card of cards) {
 nodes.randomProblem.addEventListener("click", () => {
   if (!historyReady || accountUpdatePending() || deletingReports) return;
   manualProblem = false;
+  keptDraw = null;
   roll = Math.random();
   avoidedProblem = problem?.id;
   applyDifficulties();
@@ -192,11 +198,20 @@ for (const input of levels) {
     }
     manualDifficulty = true;
     applyDifficulties();
-    // A pick made by hand survives a filter that still includes it. Only one
-    // that now hides it hands the choice back to the lobby.
-    if (manualProblem && selectedDifficulties().has(problem?.difficulty))
+    // A problem survives a filter that still includes it, whether it was
+    // picked by hand or drawn: the checkbox answered which levels to offer,
+    // not whether to throw away the problem on screen. Only a filter that now
+    // hides it hands the choice back to the lobby.
+    if (selectedDifficulties().has(problem?.difficulty)) {
+      // Kept, a drawn problem is no longer what `roll` draws under this
+      // filter, so the next `settle` would swap it. Held against the reports
+      // in hand, which while the history is still loading are the ones about
+      // to be replaced, so `settle` redraws then.
+      if (!manualProblem) keptDraw = JSON.stringify(reports);
       return;
+    }
     manualProblem = false;
+    keptDraw = null;
     roll = Math.random();
     avoidedProblem = undefined;
     // Not before the reports are in. Recommending from an empty history here
@@ -535,6 +550,10 @@ function refreshHistory() {
 /// describing history the page had already replaced.
 function settle() {
   historyReady = true;
+  // Refreshed reports that differ from the ones a kept draw came from may have
+  // just recorded it as passed, so the lobby draws again.
+  if (keptDraw !== null && keptDraw !== JSON.stringify(reports))
+    keptDraw = null;
   // The level suggestion only applies when the candidate has not already said
   // what they want. Moving their checkboxes would also hide the card they just
   // picked.
@@ -880,8 +899,9 @@ function applyDifficulties() {
 function recommend(note = "") {
   // A candidate who picked a card has answered the question this line asks, so
   // it stays answered. Naming a different problem here contradicted the card
-  // they had just selected.
-  if (manualProblem) return;
+  // they had just selected. A kept draw stands the same way until `settle`
+  // drops it.
+  if (manualProblem || keptDraw !== null) return;
   const choice = pickProblem(
     cards,
     selectedDifficulties(),