diff --git a/include/babeltrace2/graph/graph.h b/include/babeltrace2/graph/graph.h
index 9ef943d72..e4d53e6e6 100644
--- a/include/babeltrace2/graph/graph.h
+++ b/include/babeltrace2/graph/graph.h
@@ -191,7 +191,6 @@ typedef enum bt_graph_run_status {
 	BT_GRAPH_RUN_STATUS_ERROR		= __BT_FUNC_STATUS_ERROR,
 	BT_GRAPH_RUN_STATUS_MEMORY_ERROR	= __BT_FUNC_STATUS_MEMORY_ERROR,
 	BT_GRAPH_RUN_STATUS_AGAIN		= __BT_FUNC_STATUS_AGAIN,
-	BT_GRAPH_RUN_STATUS_END			= __BT_FUNC_STATUS_END,
 } bt_graph_run_status;
 
 extern bt_graph_run_status bt_graph_run(bt_graph *graph);
diff --git a/src/bindings/python/bt2/bt2/graph.py b/src/bindings/python/bt2/bt2/graph.py
index ef40014ba..a36c85d1b 100644
--- a/src/bindings/python/bt2/bt2/graph.py
+++ b/src/bindings/python/bt2/bt2/graph.py
@@ -189,14 +189,7 @@ def run_once(self):
 
     def run(self):
         status = native_bt.graph_run(self._ptr)
-
-        try:
-            utils._handle_func_status(status, 'graph object stopped running')
-        except bt2.Stop:
-            # done
-            return
-        except Exception:
-            raise
+        utils._handle_func_status(status, 'graph object stopped running')
 
     def add_interrupter(self, interrupter):
         utils._check_type(interrupter, bt2_interrupter.Interrupter)
diff --git a/src/cli/babeltrace2.c b/src/cli/babeltrace2.c
index 150b08fc1..e721ea3b7 100644
--- a/src/cli/babeltrace2.c
+++ b/src/cli/babeltrace2.c
@@ -2536,7 +2536,7 @@ int cmd_run(struct bt_config *cfg)
 
 		switch (run_status) {
 		case BT_GRAPH_RUN_STATUS_OK:
-			break;
+			goto end;
 		case BT_GRAPH_RUN_STATUS_AGAIN:
 			if (bt_interrupter_is_set(the_interrupter)) {
 				BT_CLI_LOGW_APPEND_CAUSE(
@@ -2558,8 +2558,6 @@ int cmd_run(struct bt_config *cfg)
 				}
 			}
 			break;
-		case BT_GRAPH_RUN_STATUS_END:
-			goto end;
 		default:
 			if (bt_interrupter_is_set(the_interrupter)) {
 				BT_CLI_LOGW_APPEND_CAUSE(
diff --git a/src/lib/graph/graph.c b/src/lib/graph/graph.c
index 44a5e1b4d..ed66ba89e 100644
--- a/src/lib/graph/graph.c
+++ b/src/lib/graph/graph.c
@@ -773,8 +773,15 @@ enum bt_graph_run_status bt_graph_run(struct bt_graph *graph)
 		}
 	} while (status == BT_FUNC_STATUS_OK);
 
-	if (g_queue_is_empty(graph->sinks_to_consume)) {
-		status = BT_FUNC_STATUS_END;
+	if (status == BT_FUNC_STATUS_END) {
+		/*
+		 * The last call to consume_no_check() returned
+		 * `BT_FUNC_STATUS_END`, but bt_graph_run() has no
+		 * `BT_GRAPH_RUN_STATUS_END` status: replace with
+		 * `BT_GRAPH_RUN_STATUS_OK` (success: graph ran
+		 * completely).
+		 */
+		status = BT_FUNC_STATUS_OK;
 	}
 
 end: