diff --git a/src/core/fifo_pool.ml b/src/core/fifo_pool.ml
index 1095d16e..d2757324 100644
--- a/src/core/fifo_pool.ml
+++ b/src/core/fifo_pool.ml
@@ -2,11 +2,12 @@ open Types_
 include Runner
 
 let ( let@ ) = ( @@ )
+let k_storage = Task_local_storage.Private_.Storage.k_storage
 
 type task_full = {
   f: unit -> unit;
   name: string;
-  ls: task_ls;
+  ls: Task_local_storage.storage;
 }
 
 type state = {
@@ -25,8 +26,8 @@ let schedule_ (self : state) (task : task_full) : unit =
 type around_task = AT_pair : (t -> 'a) * (t -> 'a -> unit) -> around_task
 
 let worker_thread_ (self : state) (runner : t) ~on_exn ~around_task : unit =
-  let cur_ls : task_ls ref = ref [||] in
-  TLS.set Types_.k_ls_values (Some cur_ls);
+  let cur_ls : Task_local_storage.storage ref = ref Task_local_storage.Private_.Storage.dummy in
+  TLS.set k_storage (Some cur_ls);
   TLS.get Runner.For_runner_implementors.k_cur_runner := Some runner;
 
   let (AT_pair (before_task, after_task)) = around_task in
@@ -44,7 +45,7 @@ let worker_thread_ (self : state) (runner : t) ~on_exn ~around_task : unit =
   in
 
   let run_another_task ls ~name task' =
-    let ls' = Array.copy ls in
+    let ls' = Task_local_storage.Private_.Storage.copy ls in
     schedule_ self { f = task'; name; ls = ls' }
   in
 
@@ -73,7 +74,7 @@ let worker_thread_ (self : state) (runner : t) ~on_exn ~around_task : unit =
        on_exn e bt);
     exit_span_ ();
     after_task runner _ctx;
-    cur_ls := [||]
+    cur_ls := Task_local_storage.Private_.Storage.dummy
   in
 
   let main_loop () =
@@ -130,7 +131,7 @@ let create ?(on_init_thread = default_thread_init_exit_)
     { threads = Array.make num_threads dummy; q = Bb_queue.create () }
   in
 
-  let run_async ~name f = schedule_ pool { f; name; ls = [||] } in
+  let run_async ~name ~ls f = schedule_ pool { f; name; ls } in
 
   let runner =
     Runner.For_runner_implementors.create
diff --git a/src/core/fut.ml b/src/core/fut.ml
index 6d8d264d..2c7d6896 100644
--- a/src/core/fut.ml
+++ b/src/core/fut.ml
@@ -105,7 +105,7 @@ let[@inline] fulfill_idempotent self r =
 
 (* ### combinators ### *)
 
-let spawn ?name ~on f : _ t =
+let spawn ?name ?ls ~on f : _ t =
   let fut, promise = make () in
 
   let task () =
@@ -118,13 +118,13 @@ let spawn ?name ~on f : _ t =
     fulfill promise res
   in
 
-  Runner.run_async ?name on task;
+  Runner.run_async ?name ?ls on task;
   fut
 
-let spawn_on_current_runner ?name f : _ t =
+let spawn_on_current_runner ?name ?ls f : _ t =
   match Runner.get_current_runner () with
   | None -> failwith "Fut.spawn_on_current_runner: not running on a runner"
-  | Some on -> spawn ?name ~on f
+  | Some on -> spawn ?name ?ls ~on f
 
 let reify_error (f : 'a t) : 'a or_error t =
   match peek f with
diff --git a/src/core/fut.mli b/src/core/fut.mli
index 7452f3d7..a82975f3 100644
--- a/src/core/fut.mli
+++ b/src/core/fut.mli
@@ -94,11 +94,17 @@ val is_failed : _ t -> bool
 
 (** {2 Combinators} *)
 
-val spawn : ?name:string -> on:Runner.t -> (unit -> 'a) -> 'a t
+val spawn :
+  ?name:string ->
+  ?ls:Task_local_storage.storage ->
+  on:Runner.t ->
+  (unit -> 'a) ->
+  'a t
 (** [spaw ~on f] runs [f()] on the given runner [on], and return a future that will
       hold its result. *)
 
-val spawn_on_current_runner : ?name:string -> (unit -> 'a) -> 'a t
+val spawn_on_current_runner :
+  ?name:string -> ?ls:Task_local_storage.storage -> (unit -> 'a) -> 'a t
 (** This must be run from inside a runner, and schedules
     the new task on it as well.
 
diff --git a/src/core/immediate_runner.ml b/src/core/immediate_runner.ml
index db9725f5..b3571679 100644
--- a/src/core/immediate_runner.ml
+++ b/src/core/immediate_runner.ml
@@ -1,14 +1,21 @@
+open Types_
 include Runner
 
-let run_async_ ~name f =
+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);
   let sp = Tracing_.enter_span name in
   try
     let x = f () in
     Tracing_.exit_span sp;
+    TLS.set k_ls None;
     x
   with e ->
     let bt = Printexc.get_raw_backtrace () in
     Tracing_.exit_span sp;
+    TLS.set k_ls None;
     Printexc.raise_with_backtrace e bt
 
 let runner : t =
diff --git a/src/core/moonpool.ml b/src/core/moonpool.ml
index 8031b761..c69b5581 100644
--- a/src/core/moonpool.ml
+++ b/src/core/moonpool.ml
@@ -1,8 +1,11 @@
+exception Shutdown = Runner.Shutdown
+
 let start_thread_on_some_domain f x =
   let did = Random.int (Domain_pool_.n_domains ()) in
   Domain_pool_.run_on_and_wait did (fun () -> Thread.create f x)
 
 let run_async = Runner.run_async
+let run_wait_block = Runner.run_wait_block
 let recommended_thread_count () = Domain_.recommended_number ()
 let spawn = Fut.spawn
 let spawn_on_current_runner = Fut.spawn_on_current_runner
diff --git a/src/core/moonpool.mli b/src/core/moonpool.mli
index 57c95d23..23ee52d8 100644
--- a/src/core/moonpool.mli
+++ b/src/core/moonpool.mli
@@ -15,12 +15,22 @@ module Runner = Runner
 module Immediate_runner = Immediate_runner
 module Exn_bt = Exn_bt
 
+exception Shutdown
+(** Exception raised when trying to run tasks on
+    runners that have been shut down.
+    @since NEXT_RELEASE *)
+
 val start_thread_on_some_domain : ('a -> unit) -> 'a -> Thread.t
 (** Similar to {!Thread.create}, but it picks a background domain at random
     to run the thread. This ensures that we don't always pick the same domain
     to run all the various threads needed in an application (timers, event loops, etc.) *)
 
-val run_async : ?name:string -> Runner.t -> (unit -> unit) -> unit
+val run_async :
+  ?name:string ->
+  ?ls:Task_local_storage.storage ->
+  Runner.t ->
+  (unit -> unit) ->
+  unit
 (** [run_async runner task] schedules the task to run
   on the given runner. This means [task()] will be executed
   at some point in the future, possibly in another thread.
@@ -29,20 +39,43 @@ val run_async : ?name:string -> Runner.t -> (unit -> unit) -> unit
     (since NEXT_RELEASE)
   @since 0.5 *)
 
+val run_wait_block :
+  ?name:string ->
+  ?ls:Task_local_storage.storage ->
+  Runner.t ->
+  (unit -> 'a) ->
+  'a
+(** [run_wait_block runner f] schedules [f] for later execution
+    on the runner, like {!run_async}.
+    It then blocks the current thread until [f()] is done executing,
+    and returns its result. If [f()] raises an exception, then [run_wait_block pool f]
+    will raise it as well.
+
+    {b NOTE} be careful with deadlocks (see notes in {!Fut.wait_block}
+      about the required discipline to avoid deadlocks).
+    @raise Shutdown if the runner was already shut down
+    @since NEXT_RELEASE *)
+
 val recommended_thread_count : unit -> int
 (** Number of threads recommended to saturate the CPU.
   For IO pools this makes little sense (you might want more threads than
   this because many of them will be blocked most of the time).
   @since 0.5 *)
 
-val spawn : ?name:string -> on:Runner.t -> (unit -> 'a) -> 'a Fut.t
+val spawn :
+  ?name:string ->
+  ?ls:Task_local_storage.storage ->
+  on:Runner.t ->
+  (unit -> 'a) ->
+  'a Fut.t
 (** [spawn ~on f] runs [f()] on the runner (a thread pool typically)
     and returns a future result for it. See {!Fut.spawn}.
     @param name if provided and [Trace] is present in dependencies,
       a span will be created for the future. (since 0.6)
     @since 0.5 *)
 
-val spawn_on_current_runner : ?name:string -> (unit -> 'a) -> 'a Fut.t
+val spawn_on_current_runner :
+  ?name:string -> ?ls:Task_local_storage.storage -> (unit -> 'a) -> 'a Fut.t
 (** See {!Fut.spawn_on_current_runner}.
     @param name see {!spawn}. since 0.6.
     @since 0.5 *)
diff --git a/src/core/runner.ml b/src/core/runner.ml
index 437e24c4..207ea56d 100644
--- a/src/core/runner.ml
+++ b/src/core/runner.ml
@@ -3,7 +3,7 @@ module TLS = Thread_local_storage_
 type task = unit -> unit
 
 type t = {
-  run_async: name:string -> task -> unit;
+  run_async: name:string -> ls:Task_local_storage.storage -> task -> unit;
   shutdown: wait:bool -> unit -> unit;
   size: unit -> int;
   num_tasks: unit -> int;
@@ -11,7 +11,10 @@ type t = {
 
 exception Shutdown
 
-let[@inline] run_async ?(name = "") (self : t) f : unit = self.run_async ~name f
+let[@inline] run_async ?(name = "")
+    ?(ls = Task_local_storage.Private_.Storage.create ()) (self : t) f : unit =
+  self.run_async ~name ~ls f
+
 let[@inline] shutdown (self : t) : unit = self.shutdown ~wait:true ()
 
 let[@inline] shutdown_without_waiting (self : t) : unit =
@@ -20,9 +23,9 @@ let[@inline] shutdown_without_waiting (self : t) : unit =
 let[@inline] num_tasks (self : t) : int = self.num_tasks ()
 let[@inline] size (self : t) : int = self.size ()
 
-let run_wait_block ?name self (f : unit -> 'a) : 'a =
+let run_wait_block ?name ?ls self (f : unit -> 'a) : 'a =
   let q = Bb_queue.create () in
-  run_async ?name self (fun () ->
+  run_async ?name ?ls self (fun () ->
       try
         let x = f () in
         Bb_queue.push q (Ok x)
diff --git a/src/core/runner.mli b/src/core/runner.mli
index 3b959496..5b937c09 100644
--- a/src/core/runner.mli
+++ b/src/core/runner.mli
@@ -33,16 +33,19 @@ val shutdown_without_waiting : t -> unit
 
 exception Shutdown
 
-val run_async : ?name:string -> t -> task -> unit
+val run_async :
+  ?name:string -> ?ls:Task_local_storage.storage -> t -> task -> unit
 (** [run_async pool f] schedules [f] for later execution on the runner
     in one of the threads. [f()] will run on one of the runner's
     worker threads/domains.
     @param name if provided and [Trace] is present in dependencies, a span
     will be created when the task starts, and will stop when the task is over.
     (since NEXT_RELEASE)
+    @param ls if provided, run the task with this initial local storage
     @raise Shutdown if the runner was shut down before [run_async] was called. *)
 
-val run_wait_block : ?name:string -> t -> (unit -> 'a) -> 'a
+val run_wait_block :
+  ?name:string -> ?ls:Task_local_storage.storage -> t -> (unit -> 'a) -> 'a
 (** [run_wait_block pool f] schedules [f] for later execution
     on the pool, like {!run_async}.
     It then blocks the current thread until [f()] is done executing,
@@ -62,7 +65,7 @@ module For_runner_implementors : sig
     size:(unit -> int) ->
     num_tasks:(unit -> int) ->
     shutdown:(wait:bool -> unit -> unit) ->
-    run_async:(name:string -> task -> unit) ->
+    run_async:(name:string -> ls:Task_local_storage.storage -> task -> unit) ->
     unit ->
     t
   (** Create a new runner.
diff --git a/src/core/task_local_storage.ml b/src/core/task_local_storage.ml
index 3b84a9c8..87ca1424 100644
--- a/src/core/task_local_storage.ml
+++ b/src/core/task_local_storage.ml
@@ -5,6 +5,8 @@ type 'a key = 'a ls_key
 
 let key_count_ = A.make 0
 
+type storage = task_ls
+
 let new_key (type t) ~init () : t key =
   let offset = A.fetch_and_add key_count_ 1 in
   (module struct
@@ -55,3 +57,14 @@ let with_value key x f =
   let old = get key in
   set key x;
   Fun.protect ~finally:(fun () -> set key old) f
+
+module Private_ = struct
+  module Storage = struct
+    type t = storage
+
+    let k_storage = k_ls_values
+    let[@inline] create () = [||]
+    let copy = Array.copy
+    let dummy = [||]
+  end
+end
diff --git a/src/core/task_local_storage.mli b/src/core/task_local_storage.mli
index 99a7d7b3..c2ce778a 100644
--- a/src/core/task_local_storage.mli
+++ b/src/core/task_local_storage.mli
@@ -8,6 +8,9 @@
     @since NEXT_RELEASE
 *)
 
+type storage
+(** Underlying storage for a task *)
+
 type 'a key
 (** A key used to access a particular (typed) storage slot on every task. *)
 
@@ -41,3 +44,18 @@ val with_value : 'a key -> 'a -> (unit -> 'b) -> 'b
 (** [with_value k v f] sets [k] to [v] for the duration of the call
     to [f()]. When [f()] returns (or fails), [k] is restored
     to its old value. *)
+
+(**/**)
+
+module Private_ : sig
+  module Storage : sig
+    type t = storage
+
+    val k_storage : t ref option Thread_local_storage_.key
+    val create : unit -> t
+    val copy : t -> t
+    val dummy : t
+  end
+end
+
+(**/**)
diff --git a/src/core/ws_pool.ml b/src/core/ws_pool.ml
index bb84fe75..d1fd7cf3 100644
--- a/src/core/ws_pool.ml
+++ b/src/core/ws_pool.ml
@@ -1,10 +1,10 @@
-open Types_
 module WSQ = Ws_deque_
 module A = Atomic_
 module TLS = Thread_local_storage_
 include Runner
 
 let ( let@ ) = ( @@ )
+let k_storage = Task_local_storage.Private_.Storage.k_storage
 
 module Id = struct
   type t = unit ref
@@ -17,7 +17,7 @@ end
 type task_full = {
   f: task;
   name: string;
-  ls: task_ls;
+  ls: Task_local_storage.storage;
 }
 
 type around_task = AT_pair : (t -> 'a) * (t -> 'a -> unit) -> around_task
@@ -27,7 +27,7 @@ type worker_state = {
   mutable thread: Thread.t;
   q: task_full WSQ.t;  (** Work stealing queue *)
   mutable cur_span: int64;
-  cur_ls: task_ls ref;  (** Task storage *)
+  cur_ls: Task_local_storage.storage ref;  (** Task storage *)
   rng: Random.State.t;
 }
 (** State for a given worker. Only this worker is
@@ -127,7 +127,7 @@ let run_task_now_ (self : state) ~runner (w : worker_state) ~name ~ls task :
 
   let run_another_task ls ~name task' =
     let w = find_current_worker_ () in
-    let ls' = Array.copy ls in
+    let ls' = Task_local_storage.Private_.Storage.copy ls in
     schedule_task_ self w ~name ~ls:ls' task'
   in
 
@@ -154,11 +154,11 @@ let run_task_now_ (self : state) ~runner (w : worker_state) ~name ~ls task :
 
   exit_span_ ();
   after_task runner _ctx;
-  w.cur_ls := [||]
+  w.cur_ls := Task_local_storage.Private_.Storage.dummy
 
-let[@inline] run_async_ (self : state) ~name (f : task) : unit =
+let[@inline] run_async_ (self : state) ~name ~ls (f : task) : unit =
   let w = find_current_worker_ () in
-  schedule_task_ self w ~name ~ls:[||] f
+  schedule_task_ self w ~name ~ls f
 
 (* TODO: function to schedule many tasks from the outside.
     - build a queue
@@ -276,7 +276,7 @@ type ('a, 'b) create_args =
   'a
 (** Arguments used in {!create}. See {!create} for explanations. *)
 
-let dummy_task_ = { f = ignore; ls = [||]; name = "DUMMY_TASK" }
+let dummy_task_ = { f = ignore; ls = Task_local_storage.Private_.Storage.dummy ; name = "DUMMY_TASK" }
 
 let create ?(on_init_thread = default_thread_init_exit_)
     ?(on_exit_thread = default_thread_init_exit_) ?(on_exn = fun _ _ -> ())
@@ -304,7 +304,7 @@ let create ?(on_init_thread = default_thread_init_exit_)
           cur_span = Tracing_.dummy_span;
           q = WSQ.create ~dummy:dummy_task_ ();
           rng = Random.State.make [| i |];
-          cur_ls = ref [||];
+          cur_ls = ref Task_local_storage.Private_.Storage.dummy;
         })
   in
 
@@ -326,7 +326,7 @@ let create ?(on_init_thread = default_thread_init_exit_)
   let runner =
     Runner.For_runner_implementors.create
       ~shutdown:(fun ~wait () -> shutdown_ pool ~wait)
-      ~run_async:(fun ~name f -> run_async_ pool ~name f)
+      ~run_async:(fun ~name ~ls f -> run_async_ pool ~name ~ls f)
       ~size:(fun () -> size_ pool)
       ~num_tasks:(fun () -> num_tasks_ pool)
       ()
@@ -346,7 +346,7 @@ let create ?(on_init_thread = default_thread_init_exit_)
       let thread = Thread.self () in
       let t_id = Thread.id thread in
       on_init_thread ~dom_id:dom_idx ~t_id ();
-      TLS.set k_ls_values (Some w.cur_ls);
+      TLS.set k_storage (Some w.cur_ls);
 
       (* set thread name *)
       Option.iter