diff --git a/sequence.ml b/sequence.ml
index d0cf59e..0823cd0 100644
--- a/sequence.ml
+++ b/sequence.ml
@@ -313,14 +313,19 @@ let scan f acc seq =
       let acc = ref acc in
       seq (fun elt -> let acc' = f !acc elt in k acc'; acc := acc'))
 
-(** Max element of the sequence, using the given comparison
-    function. A default element has to be provided. *)
-let max ?(lt=fun x y -> x < y) seq m =
-  fold (fun m x -> if lt m x then x else m) m seq
+let max ?(lt=fun x y -> x < y) seq =
+  let ret = ref None in
+  seq (fun x -> match !ret with
+    | None -> ret := Some x
+    | Some y -> if lt y x then ret := Some x);
+  !ret
 
-(** Min element of the sequence, using the given comparison function *)
-let min ?(lt=fun x y -> x < y) seq m =
-  fold (fun m x -> if lt x m then x else m) m seq
+let min ?(lt=fun x y -> x < y) seq =
+  let ret = ref None in
+  seq (fun x -> match !ret with
+    | None -> ret := Some x
+    | Some y -> if lt x y then ret := Some x);
+  !ret
 
 exception ExitSequence
 
diff --git a/sequence.mli b/sequence.mli
index 697a5d3..e9c4574 100644
--- a/sequence.mli
+++ b/sequence.mli
@@ -191,12 +191,14 @@ val unfoldr : ('b -> ('a * 'b) option) -> 'b -> 'a t
 val scan : ('b -> 'a -> 'b) -> 'b -> 'a t -> 'b t
   (** Sequence of intermediate results *)
 
-val max : ?lt:('a -> 'a -> bool) -> 'a t -> 'a -> 'a
-  (** Max element of the sequence, using the given comparison
-      function. A default element has to be provided. *)
+val max : ?lt:('a -> 'a -> bool) -> 'a t -> 'a option
+  (** Max element of the sequence, using the given comparison function.
+      @return None if the sequence is empty, Some [m] where [m] is the maximal
+      element otherwise *)
 
-val min : ?lt:('a -> 'a -> bool) -> 'a t -> 'a -> 'a
-  (** Min element of the sequence, using the given comparison function *)
+val min : ?lt:('a -> 'a -> bool) -> 'a t -> 'a option
+  (** Min element of the sequence, using the given comparison function.
+      see {!max} for more details. *)
 
 val take : int -> 'a t -> 'a t
   (** Take at most [n] elements from the sequence. Works on infinite