diff --git a/CHANGELOG.md b/CHANGELOG.md
index d929b82..17179c9 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,5 +5,6 @@ what it changes for someone who uses the API. CI checks that it did.
 
 ## Unreleased
 
+- `POST /tasks/:id/reopen` marks a task not done again.
 - `GET /tasks/count` says how many tasks there are, and how many are done.
 - CI checks that a pull request adds a line here.
diff --git a/README.md b/README.md
index 79997e0..f06e334 100644
--- a/README.md
+++ b/README.md
@@ -14,6 +14,7 @@ and in an adopter's first run. It is small on purpose, so a job is cheap and fas
 | GET | `/tasks/count` | Says how many tasks there are, and how many are done |
 | GET | `/tasks/:id` | Returns one task |
 | POST | `/tasks/:id/complete` | Marks a task done |
+| POST | `/tasks/:id/reopen` | Marks a task not done again |
 | DELETE | `/tasks/:id` | Removes a task |
 
 ## Working on it
diff --git a/src/server.ts b/src/server.ts
index 024a1cb..076aca6 100644
--- a/src/server.ts
+++ b/src/server.ts
@@ -10,6 +10,7 @@ import { TaskList, ValidationError } from './tasks.ts';
  *   GET    /tasks/count         how many tasks, and how many are done
  *   GET    /tasks/:id           one task
  *   POST   /tasks/:id/complete  mark a task done
+ *   POST   /tasks/:id/reopen    mark a task not done again
  *   DELETE /tasks/:id           remove a task
  */
 export function createApp(tasks: TaskList = new TaskList()): Server {
@@ -46,6 +47,7 @@ async function handle(tasks: TaskList, request: IncomingMessage, response: Serve
     return tasks.remove(id) ? send(response, 204) : send(response, 404, { error: 'not found' });
   }
   if (parts.length === 3 && parts[2] === 'complete' && method === 'POST') return found(response, tasks.complete(id));
+  if (parts.length === 3 && parts[2] === 'reopen' && method === 'POST') return found(response, tasks.reopen(id));
 
   return send(response, 404, { error: 'not found' });
 }
diff --git a/src/tasks.ts b/src/tasks.ts
index e9e84c5..c2fd36f 100644
--- a/src/tasks.ts
+++ b/src/tasks.ts
@@ -33,6 +33,13 @@ export class TaskList {
     return task;
   }
 
+  /** Mark a task not done again. Returns it, or undefined when there is no such task. */
+  reopen(id: number): Task | undefined {
+    const task = this.tasks.get(id);
+    if (task) task.done = false;
+    return task;
+  }
+
   remove(id: number): boolean {
     return this.tasks.delete(id);
   }
diff --git a/test/server.test.ts b/test/server.test.ts
index 8aaa404..cf0e0a8 100644
--- a/test/server.test.ts
+++ b/test/server.test.ts
@@ -40,6 +40,18 @@ describe('the HTTP API', () => {
     assert.equal((await call('GET', `/tasks/${id}`)).status, 404);
   });
 
+  it('reopens a task, done or not', async () => {
+    const id = (await call('POST', '/tasks', { title: 'Open again' })).json!.id as number;
+    const open = { status: 200, json: { id, title: 'Open again', done: false } };
+
+    await call('POST', `/tasks/${id}/complete`);
+    assert.deepEqual(await call('POST', `/tasks/${id}/reopen`), open);
+    assert.deepEqual(await call('POST', `/tasks/${id}/reopen`), open);
+    assert.deepEqual(await call('GET', `/tasks/${id}`), open);
+
+    await call('DELETE', `/tasks/${id}`);
+  });
+
   it('counts the tasks, and the ones that are done', async () => {
     const start = await call('GET', '/tasks/count');
     assert.equal(start.status, 200);
@@ -66,6 +78,7 @@ describe('the HTTP API', () => {
     assert.equal((await call('GET', '/nothing')).status, 404);
     assert.equal((await call('GET', '/tasks/abc')).status, 404);
     assert.equal((await call('POST', '/tasks/99/complete')).status, 404);
+    assert.equal((await call('POST', '/tasks/99/reopen')).status, 404);
     assert.equal((await call('PUT', '/tasks', { title: 'x' })).status, 405);
   });
 });
diff --git a/test/tasks.test.ts b/test/tasks.test.ts
index 85c072e..a7e5162 100644
--- a/test/tasks.test.ts
+++ b/test/tasks.test.ts
@@ -26,6 +26,18 @@ describe('the task list', () => {
     assert.equal(tasks.complete(99), undefined);
   });
 
+  it('reopens a task, and says so when there is no such task', () => {
+    const tasks = new TaskList();
+    const { id } = tasks.add('Ship it');
+    tasks.complete(id);
+    assert.deepEqual(tasks.reopen(id), { id, title: 'Ship it', done: false });
+    assert.equal(tasks.get(id)?.done, false);
+    assert.deepEqual(tasks.count(), { total: 1, done: 0 });
+
+    assert.deepEqual(tasks.reopen(id), { id, title: 'Ship it', done: false });
+    assert.equal(tasks.reopen(99), undefined);
+  });
+
   it('removes a task once', () => {
     const tasks = new TaskList();
     const { id } = tasks.add('Clean up');