diff --git a/sequence.ml b/sequence.ml
index 4906b5d..6c3f2f0 100644
--- a/sequence.ml
+++ b/sequence.ml
@@ -34,6 +34,16 @@ type (+'a, +'b) t2 = ('a -> 'b -> unit) -> unit
 (** Build a sequence from a iter function *)
 let from_iter f = f
 
+(** Call the function repeatedly until it returns None. This
+    sequence is transient, use {!persistent} if needed! *)
+let from_fun f =
+  fun k ->
+    let rec next () =
+      match f () with
+      | None -> ()
+      | Some x -> (k x; next ())
+    in next ()
+
 let empty = fun k -> ()
 
 let singleton x = fun k -> k x
@@ -117,10 +127,11 @@ let flatMap f seq =
   from_iter
     (fun k -> seq (fun x -> (f x) k))
 
-(** Insert the second element between every element of the sequence *)
-let intersperse seq elem =
-  from_iter
-    (fun k -> seq (fun x -> k x; k elem))
+(** Insert the given element between every element of the sequence *)
+let intersperse elem seq =
+  fun k ->
+    let first = ref true in
+    seq (fun x -> (if !first then first := false else k elem); k x)
 
 (** Mutable unrolled list to serve as intermediate storage *)
 module MList = struct
diff --git a/sequence.mli b/sequence.mli
index 088e5eb..1ac41ba 100644
--- a/sequence.mli
+++ b/sequence.mli
@@ -50,6 +50,10 @@ type (+'a, +'b) t2 = ('a -> 'b -> unit) -> unit
 val from_iter : (('a -> unit) -> unit) -> 'a t
   (** Build a sequence from a iter function *)
 
+val from_fun : (unit -> 'a option) -> 'a t
+  (** Call the function repeatedly until it returns None. This
+      sequence is transient, use {!persistent} if needed! *)
+
 val empty : 'a t
   (** Empty sequence *)
 
@@ -66,8 +70,7 @@ val forever : (unit -> 'b) -> 'b t
   (** Sequence that calls the given function to produce elements *)
 
 val cycle : 'a t -> 'a t
-  (** Cycle forever through the given sequence. Assume the
-      given sequence can be traversed any amount of times (not transient). *)
+  (** Cycle forever through the given sequence. *)
 
 (** {2 Consume a sequence} *)
 
@@ -119,7 +122,7 @@ val flatMap : ('a -> 'b t) -> 'a t -> 'b t
   (** Monadic bind. It applies the function to every element of the
       initial sequence, and calls [concat]. *)
 
-val intersperse : 'a t -> 'a -> 'a t
+val intersperse : 'a -> 'a t -> 'a t
   (** Insert the second element between every element of the sequence *)
 
 val persistent : 'a t -> 'a t
diff --git a/tests/test_sequence.ml b/tests/test_sequence.ml
index e0b3c5c..0d7a928 100644
--- a/tests/test_sequence.ml
+++ b/tests/test_sequence.ml
@@ -71,7 +71,7 @@ let test_flatMap () =
 
 let test_intersperse () =
   1 -- 100
-    |> (fun seq -> S.intersperse seq 0)
+    |> (fun seq -> S.intersperse 0 seq)
     |> S.take 10
     |> S.to_list
     |> OUnit.assert_equal [1;0;2;0;3;0;4;0;5;0]