diff --git a/src/core/immediate_runner.ml b/src/core/immediate_runner.ml
index b3571679..c260f439 100644
--- a/src/core/immediate_runner.ml
+++ b/src/core/immediate_runner.ml
@@ -1,11 +1,13 @@
 open Types_
 include Runner
 
+(* convenient alias *)
 let k_ls = Task_local_storage.Private_.Storage.k_storage
 
 let run_async_ ~name ~ls f =
   let cur_ls = ref ls in
   TLS.set k_ls (Some cur_ls);
+  cur_ls := ls;
   let sp = Tracing_.enter_span name in
   try
     let x = f () in
diff --git a/src/core/immediate_runner.mli b/src/core/immediate_runner.mli
index 8917d8b5..0a07d42a 100644
--- a/src/core/immediate_runner.mli
+++ b/src/core/immediate_runner.mli
@@ -11,6 +11,9 @@
     Another situation is when threads cannot be used at all (e.g. because you
     plan to call [Unix.fork] later).
 
+    {b NOTE}: this does not handle the [Suspend] effect, so [await], fork-join,
+    etc. will {b NOT} work on this runner.
+
     @since 0.5
 *)