diff --git a/internal/assignmentqueue/jetstream.go b/internal/assignmentqueue/jetstream.go
index 80de9d5..67ec0d2 100644
--- a/internal/assignmentqueue/jetstream.go
+++ b/internal/assignmentqueue/jetstream.go
@@ -186,9 +186,13 @@ func OpenConsumer(ctx context.Context, manager consumerManager, stream, subjectB
 		return nil, err
 	}
 	key := placement.Key()
+	// JetStream consumer names may not contain dots even though subjects do.
+	// Keep the placement subject hierarchical while using a stable, legal name
+	// for the durable cursor.
+	consumerName := strings.ReplaceAll(key, ".", "-")
 	consumer, err := manager.CreateOrUpdateConsumer(ctx, stream, jetstream.ConsumerConfig{
-		Name:          key,
-		Durable:       key,
+		Name:          consumerName,
+		Durable:       consumerName,
 		FilterSubject: strings.TrimSuffix(subjectBase, ".") + "." + key,
 		AckPolicy:     jetstream.AckExplicitPolicy,
 		AckWait:       5 * time.Minute,
diff --git a/internal/assignmentqueue/jetstream_test.go b/internal/assignmentqueue/jetstream_test.go
index 9c1490f..74a6857 100644
--- a/internal/assignmentqueue/jetstream_test.go
+++ b/internal/assignmentqueue/jetstream_test.go
@@ -215,7 +215,7 @@ func TestOpenConsumerUsesIndependentDurablePerPlacement(t *testing.T) {
 	if _, err := OpenConsumer(context.Background(), manager, "CI_RUNNER", "ci.assignment", taskassignment.KubernetesContainer, 4); err != nil {
 		t.Fatal(err)
 	}
-	if manager.config.Durable != "container.kubernetes" || manager.config.FilterSubject != "ci.assignment.container.kubernetes" || manager.config.AckPolicy != jetstream.AckExplicitPolicy || manager.config.MaxAckPending != 4 || manager.config.MaxDeliver != 1000 {
+	if manager.config.Name != "container-kubernetes" || manager.config.Durable != "container-kubernetes" || manager.config.FilterSubject != "ci.assignment.container.kubernetes" || manager.config.AckPolicy != jetstream.AckExplicitPolicy || manager.config.MaxAckPending != 4 || manager.config.MaxDeliver != 1000 {
 		t.Fatalf("config = %#v", manager.config)
 	}
 }