diff --git a/sdks/java/io/iceberg/src/main/java/org/apache/beam/sdk/io/iceberg/BoundedAsyncTasks.java b/sdks/java/io/iceberg/src/main/java/org/apache/beam/sdk/io/iceberg/BoundedAsyncTasks.java
index 3349c9e07fe8..2fb76bf6ac86 100644
--- a/sdks/java/io/iceberg/src/main/java/org/apache/beam/sdk/io/iceberg/BoundedAsyncTasks.java
+++ b/sdks/java/io/iceberg/src/main/java/org/apache/beam/sdk/io/iceberg/BoundedAsyncTasks.java
@@ -25,6 +25,7 @@
 import java.util.concurrent.Executors;
 import java.util.concurrent.Future;
 import java.util.function.Consumer;
+import org.apache.beam.vendor.guava.v32_1_2_jre.com.google.common.annotations.VisibleForTesting;
 import org.apache.beam.vendor.guava.v32_1_2_jre.com.google.common.base.Preconditions;
 import org.apache.beam.vendor.guava.v32_1_2_jre.com.google.common.util.concurrent.ThreadFactoryBuilder;
 
@@ -100,7 +101,9 @@ void shutdown() {
     executor.shutdownNow();
   }
 
-  private void drainFinished(Consumer<T> onDone) throws Exception {
+  /** Delivers every task that has finished, in queue order, without blocking. */
+  @VisibleForTesting
+  void drainFinished(Consumer<T> onDone) throws Exception {
     Iterator<Future<T>> iterator = active.iterator();
     while (iterator.hasNext()) {
       Future<T> future = iterator.next();
diff --git a/sdks/java/io/iceberg/src/test/java/org/apache/beam/sdk/io/iceberg/BoundedAsyncTasksTest.java b/sdks/java/io/iceberg/src/test/java/org/apache/beam/sdk/io/iceberg/BoundedAsyncTasksTest.java
index 09471c1f414f..478a616d58a2 100644
--- a/sdks/java/io/iceberg/src/test/java/org/apache/beam/sdk/io/iceberg/BoundedAsyncTasksTest.java
+++ b/sdks/java/io/iceberg/src/test/java/org/apache/beam/sdk/io/iceberg/BoundedAsyncTasksTest.java
@@ -88,14 +88,17 @@ public void testOutOfOrderCompletionDrainsFinishedTasks() throws Exception {
         },
         delivered::add);
 
-    // Wait until fast task has finished running in the background
+    // The latch fires inside the task body; the future is marked done a moment later, so a
+    // single drain can miss it. Drain until it shows up while "slow" is still blocked.
     fastTaskDone.await();
-
-    // Trigger a drain by submitting another task
     tasks.submit(() -> "noop", delivered::add);
-
-    // "fast" should have been drained while "slow" is still blocked
-    assertTrue(delivered.contains("fast"));
+    int retries = 0;
+    while (!delivered.contains("fast") && retries < 1000) {
+      Thread.sleep(1);
+      tasks.drainFinished(delivered::add);
+      retries++;
+    }
+    assertTrue("fast task was never drained", delivered.contains("fast"));
     assertFalse(delivered.contains("slow"));
 
     slowTaskHold.countDown();