diff --git a/core/CCBatch.ml b/core/CCBatch.ml
index d27de6ad..760982e6 100644
--- a/core/CCBatch.ml
+++ b/core/CCBatch.ml
@@ -1,6 +1,6 @@
 
 (*
-copyright (c) 2013-2014, simon cruanes
+copyright (c) 2013-2014, Simon Cruanes, Gabriel Radanne
 all rights reserved.
 
 redistribution and use in source and binary forms, with or without
@@ -43,12 +43,11 @@ module type S = sig
   type ('a,'b) op
   (** Operation that converts an ['a t] into a ['b t] *)
 
-  val length : (_,_) op -> int
-  (** Number of intermediate structures needed to compute this operation *)
-
   val apply : ('a,'b) op -> 'a t -> 'b t
-  (** Apply the operation to the collection.
-      @param level the optimization level, default is [OptimBase] *)
+  (** Apply the operation to the collection. *)
+
+  val apply_fold : ('a, 'b) op -> ('c -> 'b -> 'c) -> 'c -> 'a t -> 'c
+  (** Apply the operation plus a fold to the collection. *)
 
   val apply' : 'a t -> ('a,'b) op -> 'b t
   (** Flip of {!apply} *)
@@ -65,6 +64,8 @@ module type S = sig
 
   val flat_map : ('a -> 'b t) -> ('a,'b) op
 
+  val extern : ('a t -> 'b t) -> ('a,'b) op
+
   val compose : ('b,'c) op -> ('a,'b) op -> ('a,'c) op
   val (>>>) : ('a,'b) op -> ('b,'c) op -> ('a,'c) op
 end
@@ -75,12 +76,11 @@ module Make(C : COLLECTION) = struct
     | Nil : ('a,'a) op
     | Compose : ('a,'b) base_op * ('b, 'c) op -> ('a, 'c) op
   and (_,_) base_op =
-    | Id : ('a, 'a) base_op
     | Map : ('a -> 'b) -> ('a, 'b) base_op
     | Filter : ('a -> bool) -> ('a, 'a) base_op
     | FilterMap : ('a -> 'b option) -> ('a,'b) base_op
     | FlatMap : ('a -> 'b t) -> ('a,'b) base_op
-
+    | Extern : ('a t -> 'b t) -> ('a,'b) base_op
 
   (* associativity: put parenthesis on the right *)
   let rec _compose : type a b c. (a,b) op -> (b,c) op -> (a,c) op
@@ -89,20 +89,19 @@ module Make(C : COLLECTION) = struct
     | Compose (f1, f2) -> Compose (f1, _compose f2 g)
     | Nil -> g
 
-
-  (* After optimization, the op is a list of flatmaps, with maybe something else at the end *)
+  (* After optimization, the op is a list of flatmaps and external operations,
+      with maybe something else at the end *)
   type (_,_) optimized_op =
-    | Base : ('a,'b) base_op -> ('a,'b) optimized_op
-    | FlatMapPlus : ('a -> 'b t) * ('b, 'c) optimized_op -> ('a, 'c) optimized_op
-
+    | OptNil : ('a, 'a) optimized_op
+    | OptBase : ('a,'b) base_op * ('b, 'c) optimized_op -> ('a,'c) optimized_op
+    | OptFlatMap : ('a -> 'b t) * ('b, 'c) optimized_op -> ('a, 'c) optimized_op
+    | OptExtern : ('a t -> 'b t) * ('b, 'c) optimized_op -> ('a, 'c) optimized_op
 
   (* As compose, but optimize recursively on the way. *)
   let rec optimize_compose
   : type a b c. (a,b) base_op -> (b,c) op -> (a,c) optimized_op
   = fun base_op op -> match base_op, op with
-    | f, Nil -> Base f
-    | Id, Compose (f, cont) -> optimize_compose f cont
-    | f, Compose (Id, cont) -> optimize_compose f cont
+    | f, Nil -> OptBase (f, OptNil)
     | Map f, Compose (Map g, cont) ->
         optimize_compose (Map (fun x -> g (f x))) cont
     | Map f, Compose (Filter p, cont) ->
@@ -151,34 +150,45 @@ module Make(C : COLLECTION) = struct
               | None -> C.empty
               | Some y -> f' y))
           cont
+    | FlatMap f, Compose (f', tail) ->
+        merge_flat_map f (optimize_compose f' tail)
+    | Extern f, Compose (f', tail) ->
+        OptExtern (f, optimize_compose f' tail)
+    | op, Compose (Extern f', cont) ->
+        OptBase (op, optimize_compose (Extern f') cont)
 
-    (* flatmap doesn't compose with anything *)
-    | FlatMap f, Compose (f', cont) ->
-        FlatMapPlus (f, optimize_compose f' cont)
-
-
-  let rec length : type a b. (a,b) op -> int = function
-    | Nil -> 0
-    | Compose (_, cont) -> 1 + length cont
-
+  and merge_flat_map
+  : type a b c. (a -> b C.t) -> (b,c) optimized_op -> (a,c) optimized_op =
+  fun f op -> match op with
+    | OptNil -> OptFlatMap (f, op)
+    | OptFlatMap (f', cont) ->
+        merge_flat_map
+          (fun x ->
+              let a = f x in
+              C.flat_map f' a)
+          cont
+    | OptExtern  _ -> OptFlatMap (f, op)
+    | OptBase _ -> OptFlatMap (f, op)
 
   (* optimize a batch operation by fusion *)
   let optimize : type a b. (a,b) op -> (a,b) optimized_op
   = fun op -> match op with
     | Compose (a, b) -> optimize_compose a b
-    | Nil -> Base Id
+    | Nil -> OptNil
 
   let rec apply_optimized : type a b. (a,b) optimized_op -> a t -> b t
   = fun op a -> match op with
-    | Base f -> apply_base f a
-    | FlatMapPlus (f,c) -> apply_optimized c @@ C.flat_map f a
+    | OptNil -> a
+    | OptBase (f,c) -> apply_optimized c (apply_base f a)
+    | OptFlatMap (f,c) -> apply_optimized c (C.flat_map f a)
+    | OptExtern (f,c) -> apply_optimized c (f a)
   and apply_base : type a b. (a,b) base_op -> a t -> b t
   = fun op a -> match op with
     | Map f -> C.map f a
     | Filter p -> C.filter p a
     | FlatMap f -> C.flat_map f a
     | FilterMap f -> C.filter_map f a
-    | Id -> a
+    | Extern f -> f a
 
   let fusion_fold : type a b c. (a,b) base_op -> (c -> b -> c) -> c -> a -> c
   = fun op f' -> match op with
@@ -186,14 +196,22 @@ module Make(C : COLLECTION) = struct
     | Filter p -> (fun z x -> if p x then f' z x else z)
     | FlatMap f -> (fun z x -> C.fold f' z (f x))
     | FilterMap f -> (fun z x -> match f x with Some x' -> f' z x' | None -> z)
-    | Id -> f'
+    | Extern _ -> assert false
 
-  let rec apply_optimized_with_fold : type a b c. (a,b) optimized_op -> (c -> b -> c) -> c -> a t -> c
+  let rec apply_optimized_with_fold
+  : type a b c. (a,b) optimized_op -> (c -> b -> c) -> c -> a t -> c
   = fun op fold z a -> match op with
-    | Base f -> C.fold (fusion_fold f fold) z a
-    | FlatMapPlus (f,c) -> apply_optimized_with_fold c fold z @@ C.flat_map f a
-
-
+    | OptNil -> C.fold fold z a
+    | OptBase (Extern f, OptNil) ->
+        C.fold fold z (f a)
+    | OptBase (f,OptNil) ->
+        (* terminal fold *)
+        C.fold (fusion_fold f fold) z a
+    | OptBase (f,c) ->
+        (* make intermediate collection and continue *)
+        apply_optimized_with_fold c fold z (apply_base f a)
+    | OptExtern (f,c) -> apply_optimized_with_fold c fold z (f a)
+    | OptFlatMap (f,c) -> apply_optimized_with_fold c fold z (C.flat_map f a)
 
   (* optimize and run *)
   let apply op a =
@@ -213,6 +231,7 @@ module Make(C : COLLECTION) = struct
   let filter p = Compose (Filter p, Nil)
   let filter_map f = Compose (FilterMap f, Nil)
   let flat_map f = Compose (FlatMap f, Nil)
+  let extern f = Compose (Extern f, Nil)
 
   let compose f g = _compose g f
   let (>>>) f g = _compose f g
diff --git a/core/CCBatch.mli b/core/CCBatch.mli
index df10080a..7b04b692 100644
--- a/core/CCBatch.mli
+++ b/core/CCBatch.mli
@@ -35,6 +35,7 @@ module type COLLECTION = sig
   type 'a t
 
   val empty : 'a t
+  val fold : ('a -> 'b -> 'a) -> 'a -> 'b t -> 'a
   val map : ('a -> 'b) -> 'a t -> 'b t
   val filter : ('a -> bool) -> 'a t -> 'a t
   val filter_map : ('a -> 'b option) -> 'a t -> 'b t
@@ -48,13 +49,10 @@ module type S = sig
   type ('a,'b) op
   (** Operation that converts an ['a t] into a ['b t] *)
 
-  val length : (_,_) op -> int
-  (** Number of intermediate structures needed to compute this operation *)
-
   val apply : ('a,'b) op -> 'a t -> 'b t
   (** Apply the operation to the collection. *)
 
-  val apply_width_fold : ('a, 'b) op -> ('c -> 'b -> 'c) -> 'c -> 'a t -> 'c
+  val apply_fold : ('a, 'b) op -> ('c -> 'b -> 'c) -> 'c -> 'a t -> 'c
   (** Apply the operation plus a fold to the collection. *)
 
   val apply' : 'a t -> ('a,'b) op -> 'b t
@@ -72,6 +70,9 @@ module type S = sig
 
   val flat_map : ('a -> 'b t) -> ('a,'b) op
 
+  val extern : ('a t -> 'b t) -> ('a,'b) op
+  (** Use a specific function that won't be optimized *)
+
   val compose : ('b,'c) op -> ('a,'b) op -> ('a,'c) op
   val (>>>) : ('a,'b) op -> ('b,'c) op -> ('a,'c) op
 end
diff --git a/tests/bench_batch.ml b/tests/bench_batch.ml
index 90489ec3..daac17f6 100644
--- a/tests/bench_batch.ml
+++ b/tests/bench_batch.ml
@@ -6,7 +6,6 @@ module type COLL = sig
   val doubleton : 'a -> 'a -> 'a t
   val (--) : int -> int -> int t
   val equal : int t -> int t -> bool
-  val fold : (int -> int -> int) -> int -> int t -> int
 end
 
 module Make(C : COLL) = struct
@@ -31,25 +30,13 @@ module Make(C : COLL) = struct
   let ops =
     BA.(filter f1 >>> flat_map f3 >>> filter f1 >>> map f2 >>> flat_map f3 >>> map f4)
 
-  let batch_simple a =
-    let a = BA.apply ~level:BA.OptimNone ops a in
-    ignore (collect a);
-    a
-
   let batch a =
-    let a = BA.apply ~level:BA.OptimBase ops a in
-    ignore (collect a);
-    a
-
-  let batch2 a =
-    let a = BA.apply ~level:BA.OptimMergeFlatMap ops a in
+    let a = BA.apply ops a in
     ignore (collect a);
     a
 
   let bench_for ~time n =
     Printf.printf "\n\nbenchmark for %s of len %d\n" C.name n;
-    Printf.printf "optimization: from %d to %d\n"
-      (BA.length ops) (BA.length (BA.optimize ops));
     flush stdout;
     let a = C.(0 -- n) in
     (* debug
@@ -57,21 +44,18 @@ module Make(C : COLL) = struct
     CCPrint.printf "simple: %a\n" (CCArray.pp CCInt.pp) (batch_simple a);
     CCPrint.printf "batch: %a\n" (CCArray.pp CCInt.pp) (batch a);
     *)
-    assert (C.equal (batch_simple a) (naive a));
-    assert (C.equal (batch_simple a) (batch a));
+    assert (C.equal (batch a) (naive a));
     let res = Benchmark.throughputN time
       [ C.name ^ "_naive", naive, a
-      ; C.name ^ "_batch_simple", batch_simple, a
       ; C.name ^ "_batch", batch, a
-      ; C.name ^ "_batch_merge", batch2, a
       ]
     in
     Benchmark.tabulate res
 
   let bench () =
     bench_for 1 100;
-    bench_for 2 100_000;
-    bench_for 2 1_000_000;
+    bench_for 4 100_000;
+    bench_for 4 1_000_000;
     ()
 end