diff --git a/lib_eio/pool.ml b/lib_eio/pool.ml
index be5afd61e..4c8781e27 100644
--- a/lib_eio/pool.ml
+++ b/lib_eio/pool.ml
@@ -19,7 +19,7 @@ type 'a slot = 'a option ref
 module Cell = struct
   (* The possible behaviours are:
 
-     1. Suspender : In_transition -> Request            Suspender waits for a resource  
+     1. Suspender : In_transition -> Request            Suspender waits for a resource
         1.1. Resumer : Request -> Finished              Resumer then providers a resource
         1.2. Suspender : Request -> Finished            Suspender cancels
      2. Resumer : In_transition -> Resource             Resumer provides a spare resource
@@ -89,11 +89,10 @@ let cancel segment cell =
   | In_transition | Resource _ -> assert false          (* Can't get here from [Request]. *)
 
 (* If [t] is under capacity, add another (empty) slot. *)
-let rec maybe_add_slot t =
-  let current = Atomic.get t.slots in
+let rec maybe_add_slot t current =
   if current < t.max_slots then (
     if Atomic.compare_and_set t.slots current (current + 1) then add t (ref None)
-    else maybe_add_slot t       (* Concurrent update; try again *)
+    else maybe_add_slot t (Atomic.get t.slots)      (* Concurrent update; try again *)
   )
 
 (* [run_with t f slot] ensures that [slot] contains a valid resource and then runs [f resource] with it.
@@ -114,7 +113,7 @@ let run_with t f slot =
         f x
     end
   with
-  | r -> 
+  | r ->
     add t slot;
     r
   | exception ex ->
@@ -122,17 +121,36 @@ let run_with t f slot =
     add t slot;
     Printexc.raise_with_backtrace ex bt
 
-let use t f =
+(* Creates a fresh resource [x], runs [f x], then disposes of [x] *)
+let run_new_and_dispose t f =
+  let x = t.alloc () in
+  match f x with
+  | r ->
+    t.dispose x;
+    r
+  | exception ex ->
+    let bt = Printexc.get_raw_backtrace () in
+    t.dispose x;
+    Printexc.raise_with_backtrace ex bt
+
+let use t ?(never_block=false) f =
   let segment, cell = Q.next_suspend t.q in
   match Atomic.get cell with
   | Finished | Request _ -> assert false
   | Resource slot ->
     Atomic.set cell Finished;   (* Allow value to be GC'd *)
     run_with t f slot
-  | In_transition ->
-      (* It would have been better if more resources were available.
-         If we still have capacity, add a new slot now. *)
-      maybe_add_slot t;
+  | In_transition -> (
+    let current = Atomic.get t.slots in
+    match current < t.max_slots with
+    | false when never_block ->
+      (* We are at capacity, but cannot block.
+         Create a new resource to run f but don't add it to the pool. *)
+      Atomic.set cell Finished;
+      run_new_and_dispose t f
+    | can_add ->
+      (* Create a slot if not at capacity. *)
+      if can_add then maybe_add_slot t current;
       (* No item is available right now. Start waiting *)
       let slot =
         Suspend.enter_unchecked (fun ctx enqueue ->
@@ -156,3 +174,4 @@ let use t f =
       in
       (* assert (Atomic.get cell = Finished); *)
       run_with t f slot
+  )
\ No newline at end of file
diff --git a/lib_eio/pool.mli b/lib_eio/pool.mli
index d299b714e..5437134d5 100644
--- a/lib_eio/pool.mli
+++ b/lib_eio/pool.mli
@@ -38,6 +38,12 @@ val create :
                    If it raises, the exception is passed on to the user,
                    but resource is still considered to have been disposed. *)
 
-val use : 'a t -> ('a -> 'b) -> 'b
+val use : 'a t -> ?never_block:bool -> ('a -> 'b) -> 'b
 (** [use t fn] waits for some resource [x] to be available and then runs [f x].
-    Afterwards (on success or error), [x] is returned to the pool. *)
+    Afterwards (on success or error), [x] is returned to the pool.
+
+    @param never_block If [true] and the pool has reached maximum capacity,
+                       then a fresh resource is created to ensure that this [use]
+                       call does not wait for a resource to become available.
+                       This resource is immediately disposed after [f x] returns.
+    *)
diff --git a/tests/pool.md b/tests/pool.md
index b391b50d0..ce547c131 100644
--- a/tests/pool.md
+++ b/tests/pool.md
@@ -77,6 +77,33 @@ Two uses with a capacity of 2; they run in parallel:
 - : unit = ()
 ```
 
+Capacity of 1; two uses that cannot block and two normal uses; first 2 are parallel, next 2 are sequential:
+
+```ocaml
+# Eio_mock.Backend.run @@ fun () ->
+  let p0, r0 = Promise.create () in
+  let p1, r1 = Promise.create () in
+  let t = create 1 [p0; p1] in
+  Fiber.all [
+    (fun () -> P.use t ~never_block:true (fun x -> traceln "A: using item %d" x; Fiber.yield (); traceln "A done"));
+    (fun () -> P.use t ~never_block:true (fun x -> traceln "B: using item %d" x; Fiber.yield (); traceln "B done"));
+    (fun () -> P.use t (fun x -> traceln "C: using item %d" x; Fiber.yield (); traceln "C done"));
+    (fun () -> P.use t (fun x -> traceln "D: using item %d" x; Fiber.yield (); traceln "D done"));
+    (fun () -> Promise.resolve r0 (Ok 0); Promise.resolve r1 (Ok 1));
+  ];
++Creating item 0
++Creating item 1
++A: using item 1
++B: using item 0
++A done
++B done
++C: using item 1
++C done
++D: using item 1
++D done
+- : unit = ()
+```
+
 ## Cancellation
 
 ```ocaml