diff --git a/tests/remote-runners-doors.test.mts b/tests/remote-runners-doors.test.mts
index f9a6d05..23cd1a1 100644
--- a/tests/remote-runners-doors.test.mts
+++ b/tests/remote-runners-doors.test.mts
@@ -483,12 +483,16 @@ test('an upload refused in the middle of its body is answered, marked: never a r
   send(c)
   const { m, lease } = await runningLease(c)
   /** A PUT whose body is megabytes of `chunk()`, sent as it is read: still on its way when home finds what is wrong with it. */
+  let pulled = 0
   const streamed = (headers: Record<string, string>, chunk: () => Uint8Array, chunks: number) => {
     let sent = 0
     const body = new ReadableStream<Uint8Array>({
       pull(controller) {
         if (sent++ >= chunks) controller.close()
-        else controller.enqueue(chunk())
+        else {
+          pulled++
+          controller.enqueue(chunk())
+        }
       },
     })
     return fetch(`${m.home}/api/runners/v1/attempts/${lease.attemptId}/files/submission.csv`, {
@@ -526,9 +530,13 @@ test('an upload refused in the middle of its body is answered, marked: never a r
   const { cancelRemote } = await import('../server/src/competitions/remote/release.js')
   assert.equal(cancelRemote(queueRow(lease.submissionId)!, 'teacher'), true)
   const started = Date.now()
+  pulled = 0
   const late = await streamed({ 'content-encoding': 'gzip', 'x-colloq-sha256': 'c'.repeat(64), 'x-colloq-bytes': '100' }, noise, 1024)
   assert.equal(late.status, 409)
-  assert.ok(Date.now() - started < 1_500, `answered before the sixty-four megabytes were sent (${Date.now() - started} ms)`)
+  // Counted in chunks, not milliseconds, which a loaded runner stretches: a body home does not read stops at what the
+  // sockets' buffers hold, a few megabytes, while one it drained would have been sent whole before the answer.
+  assert.ok(pulled < 512, `answered before the sixty-four megabytes were sent (${pulled} of 1024 chunks, ${Date.now() - started} ms)`)
+  assert.ok(Date.now() - started < 10_000, `answered at once, not after a timeout (${Date.now() - started} ms)`)
   assert.equal(parseRemoteErrorReply(await late.json()).error, 'revoked')
 })
 
diff --git a/tests/runner-agent-lifecycle.test.mts b/tests/runner-agent-lifecycle.test.mts
index 548caa5..5417c1f 100644
--- a/tests/runner-agent-lifecycle.test.mts
+++ b/tests/runner-agent-lifecycle.test.mts
@@ -618,6 +618,8 @@ test('a drain lets a held hidden-test run finish: what it reads stays until it h
     return { json: syncReply({ seq: lease.seq, leases, trusted: true, want: { revisions: [{ id: REVISION.id, ref: REVISION.ref, layers: LAYERS, gpu: false }], data, bundles: [] } }), delayMs: leases.length > 0 ? 0 : 20 }
   }
   const { agent, seam, docker } = agentFor(home)
+  // The run waits for the read of its /data below: one that ended at once could have its tree removed under the read.
+  seam.next = 'wait'
   // The lease's image is checked once more right before its run (images.ts · verify), before it links the hidden test: held there, where a drain can come.
   let verifying = 0
   let release!: () => void
@@ -636,12 +638,14 @@ test('a drain lets a held hidden-test run finish: what it reads stays until it h
     await waitFor(() => seam.runs.length === 1, 'the hidden-test run, after the drain')
     assert.equal(seam.runs[0]!.sealedInputs, true)
     assert.equal(fs.readFileSync(path.join(seam.runs[0]!.dataDir, 'test.csv'), 'utf8'), 'id\n9\n')
+    seam.release()
     await waitFor(() => !fs.existsSync(path.join(layout.leasesDir, `${lease.attemptId}.json`)), 'the run settled')
     assert.ok(!home.calls.some((call) => call.path.endsWith(`/attempts/${lease.attemptId}/outcome`) && (call.body as { kind: string }).kind === 'declined'), 'the drain declined a run it was to finish')
     // Settled, it reads nothing more: a draining machine keeps none of the hidden test.
     await waitFor(() => fs.readdirSync(path.join(competitionsDir, '.sealed')).length === 0, 'the hidden test gone once the run is done')
   } finally {
     release()
+    seam.release()
     await agent.stop()
     await running
     await home.close()