diff --git a/tests/core/t_heap.ml b/tests/core/t_heap.ml
index 6c2ee2ed..9a3e96a0 100644
--- a/tests/core/t_heap.ml
+++ b/tests/core/t_heap.ml
@@ -2,106 +2,121 @@ open CCHeap
 module T = (val Containers_testlib.make ~__FILE__ ())
 include T
 
+(* A QCheck generator for natural numbers that are not too large (larger than
+ * [small_nat] but smaller than [big_nat]), with a bias towards smaller numbers.
+ * This also happens to be what QCheck uses for picking a length for a list
+ * generated by [QCheck.list].
+ * QCheck defines this generator under the name [nat] but does not expose it. *)
+let medium_nat =
+  Q.make ~print:Q.Print.int ~shrink:Q.Shrink.int ~small:(fun _ -> 1)
+    (fun st ->
+       let p = Random.State.float st 1. in
+       if p < 0.5 then Random.State.int st 10
+       else if p < 0.75 then Random.State.int st 100
+       else if p < 0.95 then Random.State.int st 1_000
+       else Random.State.int st 10_000
+    )
+
 module H = CCHeap.Make (struct
   type t = int
-
   let leq x y = x <= y
 end)
 
-let rec is_sorted l =
-  match l with
-  | [ _ ] | [] -> true
-  | x :: (y :: _ as l') -> x <= y && is_sorted l'
-
-let extract_list = H.to_list_sorted;;
-
-t @@ fun () ->
-let h = H.of_list [ 5; 3; 4; 1; 42; 0 ] in
-let h, x = H.take_exn h in
-assert_equal ~printer:string_of_int 0 x;
-let h, x = H.take_exn h in
-assert_equal ~printer:string_of_int 1 x;
-let h, x = H.take_exn h in
-assert_equal ~printer:string_of_int 3 x;
-let h, x = H.take_exn h in
-assert_equal ~printer:string_of_int 4 x;
-let h, x = H.take_exn h in
-assert_equal ~printer:string_of_int 5 x;
-let h, x = H.take_exn h in
-assert_equal ~printer:string_of_int 42 x;
-assert_raises
-  (function
-    | H.Empty -> true
-    | _ -> false)
-  (fun () -> H.take_exn h);
-true
 ;;
 
-q ~count:30
-  Q.(list_of_size Gen.(return 1_000) int)
+t ~name:"of_list, take_exn" @@ fun () ->
+  let h = H.of_list [ 5; 4; 3; 4; 1; 42; 0 ] in
+  let h, x = H.take_exn h in
+  assert_equal ~printer:string_of_int 0 x;
+  let h, x = H.take_exn h in
+  assert_equal ~printer:string_of_int 1 x;
+  let h, x = H.take_exn h in
+  assert_equal ~printer:string_of_int 3 x;
+  let h, x = H.take_exn h in
+  assert_equal ~printer:string_of_int 4 x;
+  let h, x = H.take_exn h in
+  assert_equal ~printer:string_of_int 4 x;
+  let h, x = H.take_exn h in
+  assert_equal ~printer:string_of_int 5 x;
+  let h, x = H.take_exn h in
+  assert_equal ~printer:string_of_int 42 x;
+  assert_raises ((=) H.Empty) (fun () -> H.take_exn h);
+  true
+;;
+
+q ~name:"of_list, to_list"
+  ~count:30
+  Q.(list medium_nat)
   (fun l ->
-    (* put elements into a heap *)
-    let h = H.of_iter (Iter.of_list l) in
-    assert_equal 1_000 (H.size h);
-    let l' = extract_list h in
-    is_sorted l')
+    (l |> H.of_list |> H.to_list |> List.sort CCInt.compare)
+    = (l |> List.sort CCInt.compare))
 ;;
 
-(* test filter *)
-q ~count:30
-  Q.(list_of_size Gen.(return 1_000) int)
+q ~name:"of_list, to_list_sorted"
+  ~count:30
+  Q.(list medium_nat)
   (fun l ->
-    (* put elements into a heap *)
-    let h = H.of_iter (Iter.of_list l) in
-    let h = H.filter (fun x -> x mod 2 = 0) h in
-    assert (H.to_iter h |> Iter.for_all (fun x -> x mod 2 = 0));
-    let l' = extract_list h in
-    is_sorted l')
+    (l |> H.of_list |> H.to_list_sorted)
+    = (l |> List.sort CCInt.compare))
 ;;
 
-q
-  Q.(list_of_size Gen.(return 1_000) int)
+(* The remaining tests assume the correctness of
+   [of_list], [to_list], [to_list_sorted]. *)
+
+q ~name:"size"
+  ~count:30
+  Q.(list_of_size Gen.small_nat medium_nat)
   (fun l ->
-    (* put elements into a heap *)
-    let h = H.of_iter (Iter.of_list l) in
-    let l' = H.to_iter_sorted h |> Iter.to_list in
-    is_sorted l')
+    (l |> H.of_list |> H.size)
+    = (l |> List.length))
 ;;
 
-q
-  Q.(list int)
+q ~name:"filter"
+  Q.(list medium_nat)
   (fun l ->
-    extract_list (H.of_list l) = extract_list (H.of_gen (CCList.to_gen l)))
+    let p = (fun x -> x mod 2 = 0) in
+    let l' = l |> H.of_list |> H.filter p |> H.to_list in
+    List.for_all p l' && List.length l' = List.length (List.filter p l))
 ;;
 
-q
-  Q.(list int)
+q ~name:"to_iter_sorted"
+  Q.(list_of_size Gen.small_nat medium_nat)
   (fun l ->
-    let h = H.of_list l in
-    H.to_gen h |> CCList.of_gen |> List.sort Stdlib.compare
-    = (H.to_list h |> List.sort Stdlib.compare))
+    (l |> H.of_list |> H.to_iter_sorted |> Iter.to_list)
+    = (l |> List.sort CCInt.compare))
 ;;
 
-q
-  Q.(list int)
+q ~name:"of_gen"
+  Q.(list_of_size Gen.small_nat medium_nat)
   (fun l ->
-    let h = H.of_list l in
-    H.to_string string_of_int h
-    = (List.sort Stdlib.compare l |> List.map string_of_int |> String.concat ","))
+    (l |> CCList.to_gen |> H.of_gen |> H.to_list_sorted)
+    = (l |> List.sort CCInt.compare))
 ;;
 
-q
-  Q.(list int)
+q ~name:"to_gen"
+  Q.(list_of_size Gen.small_nat medium_nat)
   (fun l ->
-    let h = H.of_list l in
-    H.to_string ~sep:" " string_of_int h
-    = (List.sort Stdlib.compare l |> List.map string_of_int |> String.concat " "))
+    (l |> H.of_list |> H.to_gen |> CCList.of_gen |> List.sort CCInt.compare)
+    = (l |> List.sort CCInt.compare))
 ;;
 
-q
-  Q.(list_of_size Gen.(return 1_000) int)
+q ~name:"to_string with default sep"
+  Q.(list_of_size Gen.small_nat medium_nat)
+  (fun l ->
+    (l |> H.of_list |> H.to_string string_of_int)
+    = (l |> List.sort CCInt.compare |> List.map string_of_int |> String.concat ","))
+;;
+
+q ~name:"to_string with space as sep"
+  Q.(list_of_size Gen.small_nat medium_nat)
+  (fun l ->
+    (l |> H.of_list |> H.to_string ~sep:" " string_of_int)
+    = (l |> List.sort CCInt.compare |> List.map string_of_int |> String.concat " "))
+;;
+
+q ~name:"Make_from_compare"
+  Q.(list_of_size Gen.small_nat medium_nat)
   (fun l ->
     let module H' = Make_from_compare (CCInt) in
-    let h = H'.of_list l in
-    let l' = H'.to_list_sorted h in
-    is_sorted l')
+    (l |> H'.of_list |> H'.to_list_sorted)
+    = (l |> List.sort CCInt.compare))