diff --git a/leftistheap.ml b/leftistheap.ml
index 0c1c5675..a5fc3e34 100644
--- a/leftistheap.ml
+++ b/leftistheap.ml
@@ -23,7 +23,7 @@ OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *)
 
-(** {1 Leftist Heaps *)
+(** {1 Leftist Heaps} *)
 
 (** Polymorphic implementation, following Okasaki *)
 
@@ -36,11 +36,16 @@ and 'a tree =
   | Empty
   | Node of int * 'a * 'a tree * 'a tree
 
-let empty ~leq =
+let empty_with ~leq =
   { tree = Empty;
     leq;
   }
 
+let empty =
+  { tree = Empty;
+    leq = (fun x y -> x <= y);
+  }
+
 let is_empty heap =
   match heap.tree with
   | Empty -> true
diff --git a/leftistheap.mli b/leftistheap.mli
index b01f4741..7565509a 100644
--- a/leftistheap.mli
+++ b/leftistheap.mli
@@ -23,16 +23,19 @@ OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *)
 
-(** {1 Leftist Heaps *)
+(** {1 Leftist Heaps} *)
 
 (** Polymorphic implementation, following Okasaki *)
 
 type 'a t
   (** Heap containing values of type 'a *)
 
-val empty : leq:('a -> 'a -> bool) -> 'a t
-  (** Empty heap. The function is used to check whether
-      the first element is smaller than the second. *)
+val empty_with : leq:('a -> 'a -> bool) -> 'a t
+  (** Empty heap. The function is used to check whether the first element is
+      smaller than the second. *)
+
+val empty : 'a t
+  (** Empty heap using Pervasives.compare *)
 
 val is_empty : _ t -> bool
   (** Is the heap empty? *)
diff --git a/tests/test_leftistheap.ml b/tests/test_leftistheap.ml
index e5f124c4..ee93eb56 100644
--- a/tests/test_leftistheap.ml
+++ b/tests/test_leftistheap.ml
@@ -3,7 +3,7 @@
 
 open OUnit
 
-let empty = Leftistheap.empty ~leq:(fun i j -> i <= j)
+let empty = Leftistheap.empty
 
 let test1 () =
   let h = Leftistheap.of_seq empty (Sequence.of_list [5;3;4;1;42;0]) in
@@ -27,6 +27,7 @@ let rec is_sorted l = match l with
   | [] -> true
   | x::((y::_) as l') -> x <= y && is_sorted l'
 
+(* extract the content of the heap into a list *)
 let extract_list heap =
   let rec recurse acc h =
     if Leftistheap.is_empty h
@@ -43,6 +44,7 @@ let test_sort () =
   let l = Sequence.to_rev_list (Sequence.take n (Sequence.random_int n)) in
   (* put elements into a heap *)
   let h = Leftistheap.of_seq empty (Sequence.of_list l) in
+  OUnit.assert_equal n (Leftistheap.size h);
   let l' = extract_list h in
   OUnit.assert_bool "sorted" (is_sorted l');
   ()