diff --git a/block.c b/block.c
index 3fe12b6..60820bf 100644
--- a/block.c
+++ b/block.c
@@ -4195,6 +4195,7 @@ void *block_job_create(const BlockJobType *job_type, BlockDriverState *bs,
     job->bs            = bs;
     job->cb            = cb;
     job->opaque        = opaque;
+    job->busy          = true;
     bs->job = job;
     return job;
 }
@@ -4244,3 +4245,13 @@ void block_job_cancel_sync(BlockJob *job)
         qemu_aio_wait();
     }
 }
+
+void block_job_sleep_ns(BlockJob *job, QEMUClock *clock, int64_t ns)
+{
+    /* Check cancellation *before* setting busy = false, too!  */
+    if (!block_job_is_cancelled(job)) {
+        job->busy = false;
+        co_sleep_ns(clock, ns);
+        job->busy = true;
+    }
+}
diff --git a/block/stream.c b/block/stream.c
index 0116450..a2bb854 100644
--- a/block/stream.c
+++ b/block/stream.c
@@ -100,14 +100,18 @@ static void coroutine_fn stream_run(void *opaque)
     }
 
     for (sector_num = 0; sector_num < end; sector_num += n) {
+        uint64_t delay_ns = 0;
         bool copy;
 
-retry:
+wait:
+        /* Note that even when no rate limit is applied we need to yield
+         * with no pending I/O here so that qemu_aio_flush() returns.
+         */
+        block_job_sleep_ns(&s->common, rt_clock, delay_ns);
         if (block_job_is_cancelled(&s->common)) {
             break;
         }
 
-        s->common.busy = true;
         ret = bdrv_co_is_allocated(bs, sector_num,
                                    STREAM_BUFFER_SIZE / BDRV_SECTOR_SIZE, &n);
         if (ret == 1) {
@@ -123,13 +127,9 @@ retry:
         trace_stream_one_iteration(s, sector_num, n, ret);
         if (ret >= 0 && copy) {
             if (s->common.speed) {
-                uint64_t delay_ns = ratelimit_calculate_delay(&s->limit, n);
+                delay_ns = ratelimit_calculate_delay(&s->limit, n);
                 if (delay_ns > 0) {
-                    s->common.busy = false;
-                    co_sleep_ns(rt_clock, delay_ns);
-
-                    /* Recheck cancellation and that sectors are unallocated */
-                    goto retry;
+                    goto wait;
                 }
             }
             ret = stream_populate(bs, sector_num, n, buf);
@@ -141,12 +141,6 @@ retry:
 
         /* Publish progress */
         s->common.offset += n * BDRV_SECTOR_SIZE;
-
-        /* Note that even when no rate limit is applied we need to yield
-         * with no pending I/O here so that qemu_aio_flush() returns.
-         */
-        s->common.busy = false;
-        co_sleep_ns(rt_clock, 0);
     }
 
     if (!base) {
diff --git a/block_int.h b/block_int.h
index 12fba69..c1f8649 100644
--- a/block_int.h
+++ b/block_int.h
@@ -97,18 +97,15 @@ struct BlockJob {
     /**
      * Set to true if the job should cancel itself.  The flag must
      * always be tested just before toggling the busy flag from false
-     * to true.  After a job has detected that the cancelled flag is
-     * true, it should not anymore issue any I/O operation to the
-     * block device.
+     * to true.  After a job has been cancelled, it should only yield
+     * if #qemu_aio_wait will ("sooner or later") reenter the coroutine.
      */
     bool cancelled;
 
     /**
      * Set to false by the job while it is in a quiescent state, where
-     * no I/O is pending and cancellation can be processed without
-     * issuing new I/O.  The busy flag must be set to false when the
-     * job goes to sleep on any condition that is not detected by
-     * #qemu_aio_wait, such as a timer.
+     * no I/O is pending and the job has yielded on any condition
+     * that is not detected by #qemu_aio_wait, such as a timer.
      */
     bool busy;
 
@@ -361,6 +358,17 @@ void *block_job_create(const BlockJobType *job_type, BlockDriverState *bs,
                        BlockDriverCompletionFunc *cb, void *opaque);
 
 /**
+ * block_job_sleep_ns:
+ * @job: The job that calls the function.
+ * @clock: The clock to sleep on.
+ * @ns: How many nanoseconds to stop for.
+ *
+ * Put the job to sleep (assuming that it wasn't canceled) for @ns
+ * nanoseconds.  Canceling the job will interrupt the wait immediately.
+ */
+void block_job_sleep_ns(BlockJob *job, QEMUClock *clock, int64_t ns);
+
+/**
  * block_job_complete:
  * @job: The job being completed.
  * @ret: The status code.
