diff --git a/CHANGELOG.md b/CHANGELOG.md
index 0fbe74e..82f4d48 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,7 @@ what it changes for someone who uses the API. CI checks that it did.
 
 ## Unreleased
 
+- `DELETE /tasks/done` removes every task that is done, and says how many it removed. (#6)
 - `PATCH /tasks/:id` renames a task, body `{"title": "..."}`, and answers with the task. (#5) (#7)
 - `GET /tasks/count` says how many tasks there are, and how many are done.
 - CI checks that a pull request adds a line here that ends with its number. (#4)
diff --git a/README.md b/README.md
index 8345f85..5cf67e9 100644
--- a/README.md
+++ b/README.md
@@ -12,6 +12,7 @@ and in an adopter's first run. It is small on purpose, so a job is cheap and fas
 | GET | `/tasks` | Lists every task |
 | POST | `/tasks` | Adds a task, body `{"title": "..."}` |
 | GET | `/tasks/count` | Says how many tasks there are, and how many are done |
+| DELETE | `/tasks/done` | Removes every task that is done, and says how many |
 | GET | `/tasks/:id` | Returns one task |
 | PATCH | `/tasks/:id` | Changes a task's title, body `{"title": "..."}` |
 | POST | `/tasks/:id/complete` | Marks a task done |
diff --git a/src/server.ts b/src/server.ts
index a4a30f2..2a46507 100644
--- a/src/server.ts
+++ b/src/server.ts
@@ -8,6 +8,7 @@ import { TaskList, ValidationError } from './tasks.ts';
  *   GET    /tasks               every task
  *   POST   /tasks               add a task, body {"title": "..."}
  *   GET    /tasks/count         how many tasks, and how many are done
+ *   DELETE /tasks/done          remove every task that is done, and say how many
  *   GET    /tasks/:id           one task
  *   PATCH  /tasks/:id           change a task's title, body {"title": "..."}
  *   POST   /tasks/:id/complete  mark a task done
@@ -38,6 +39,7 @@ async function handle(tasks: TaskList, request: IncomingMessage, response: Serve
   }
 
   if (parts.length === 2 && parts[1] === 'count' && method === 'GET') return send(response, 200, tasks.count());
+  if (parts.length === 2 && parts[1] === 'done' && method === 'DELETE') return send(response, 200, { removed: tasks.removeDone() });
 
   const id = Number(parts[1]);
   if (!Number.isInteger(id) || id < 1) return send(response, 404, { error: 'not found' });
diff --git a/src/tasks.ts b/src/tasks.ts
index 32d5f4f..08b1fff 100644
--- a/src/tasks.ts
+++ b/src/tasks.ts
@@ -49,6 +49,15 @@ export class TaskList {
     return this.tasks.delete(id);
   }
 
+  /** Remove every task that is done. Returns how many it removed. */
+  removeDone(): number {
+    let removed = 0;
+    for (const task of this.tasks.values()) {
+      if (task.done && this.tasks.delete(task.id)) removed++;
+    }
+    return removed;
+  }
+
   /** How many tasks there are, and how many of them are done. */
   count(): { total: number; done: number } {
     let done = 0;
diff --git a/test/server.test.ts b/test/server.test.ts
index 0a143c8..0e2a2fe 100644
--- a/test/server.test.ts
+++ b/test/server.test.ts
@@ -57,6 +57,32 @@ describe('the HTTP API', () => {
     assert.deepEqual(await call('GET', '/tasks/count'), { status: 200, json: { total, done } });
   });
 
+  it('removes every task that is done, and keeps the rest', async () => {
+    await call('DELETE', '/tasks/done');
+    const first = (await call('POST', '/tasks', { title: 'Done one' })).json!.id as number;
+    const open = (await call('POST', '/tasks', { title: 'Still open' })).json!.id as number;
+    const third = (await call('POST', '/tasks', { title: 'Done two' })).json!.id as number;
+    await call('POST', `/tasks/${first}/complete`);
+    await call('POST', `/tasks/${third}/complete`);
+
+    assert.deepEqual(await call('DELETE', '/tasks/done'), { status: 200, json: { removed: 2 } });
+    assert.equal((await call('GET', `/tasks/${first}`)).status, 404);
+    assert.equal((await call('GET', `/tasks/${third}`)).status, 404);
+    assert.deepEqual(await call('GET', `/tasks/${open}`), { status: 200, json: { id: open, title: 'Still open', done: false } });
+
+    await call('DELETE', `/tasks/${open}`);
+  });
+
+  it('answers removed 0 when no task is done', async () => {
+    await call('DELETE', '/tasks/done');
+    const id = (await call('POST', '/tasks', { title: 'Not done yet' })).json!.id as number;
+
+    assert.deepEqual(await call('DELETE', '/tasks/done'), { status: 200, json: { removed: 0 } });
+    assert.deepEqual((await call('GET', `/tasks/${id}`)).json, { id, title: 'Not done yet', done: false });
+
+    await call('DELETE', `/tasks/${id}`);
+  });
+
   it('refuses a task without a title, and a body that is not JSON', async () => {
     assert.deepEqual(await call('POST', '/tasks', { title: '' }), { status: 400, json: { error: 'title must be text' } });
     assert.deepEqual(await call('POST', '/tasks', 'not json'), { status: 400, json: { error: 'the body must be JSON' } });
diff --git a/test/tasks.test.ts b/test/tasks.test.ts
index e36c1c7..1650aa1 100644
--- a/test/tasks.test.ts
+++ b/test/tasks.test.ts
@@ -63,6 +63,33 @@ describe('the task list', () => {
     assert.equal(tasks.get(id), undefined);
   });
 
+  it('removes the tasks that are done, says how many, and keeps the rest', () => {
+    const tasks = new TaskList();
+    const first = tasks.add('Write the spec');
+    const second = tasks.add('Review it');
+    const third = tasks.add('Ship it');
+    tasks.complete(first.id);
+    tasks.complete(third.id);
+
+    assert.equal(tasks.removeDone(), 2);
+    assert.deepEqual(tasks.all(), [{ id: second.id, title: 'Review it', done: false }]);
+    assert.deepEqual(tasks.count(), { total: 1, done: 0 });
+    assert.equal(tasks.add('Celebrate').id, third.id + 1);
+  });
+
+  it('removes nothing when no task is done', () => {
+    const tasks = new TaskList();
+    assert.equal(tasks.removeDone(), 0);
+
+    const { id } = tasks.add('Write the spec');
+    assert.equal(tasks.removeDone(), 0);
+    assert.deepEqual(tasks.all(), [{ id, title: 'Write the spec', done: false }]);
+
+    tasks.complete(id);
+    assert.equal(tasks.removeDone(), 1);
+    assert.equal(tasks.removeDone(), 0);
+  });
+
   it('counts the tasks, and the ones that are done', () => {
     const tasks = new TaskList();
     assert.deepEqual(tasks.count(), { total: 0, done: 0 });