diff --git a/enum.ml b/enum.ml
index d1274a16..31067fa0 100644
--- a/enum.ml
+++ b/enum.ml
@@ -399,9 +399,10 @@ let intersperse x enum =
 (** Cartesian product *)
 let product a b =
   fun () ->
-    (* [a] is the outer relation *)
-    let gen_a = a () in
-    try
+    if is_empty a || is_empty b then fun () -> raise EOG
+    else
+      (* [a] is the outer relation *)
+      let gen_a = a () in
       (* current element of [a] *)
       let cur_a = ref (gen_a ()) in
       let gen_b = ref (b ()) in
@@ -414,8 +415,6 @@ let product a b =
           next ()
       in
       next
-    with EOG ->
-      raise EOG  (* [a] is empty *)
 
 let permutations enum =
   failwith "not implemented" (* TODO *)
diff --git a/enum.mli b/enum.mli
index 3e44dce5..4406b45f 100644
--- a/enum.mli
+++ b/enum.mli
@@ -109,8 +109,7 @@ val drop : int -> 'a t -> 'a t
   (** Drop n elements *)
 
 val filter : ('a -> bool) -> 'a t -> 'a t
-  (** Filter out elements that do not satisfy the predicate. The outer
-      enum must be finite. *)
+  (** Filter out elements that do not satisfy the predicate.  *)
 
 val takeWhile : ('a -> bool) -> 'a t -> 'a t
   (** Take elements while they satisfy the predicate *)
@@ -133,7 +132,8 @@ val zipIndex : 'a t -> (int * 'a) t
 (** {2 Complex combinators} *)
 
 val round_robin : 'a t t -> 'a t
-  (** Pick elements fairly in each sub-enum *)
+  (** Pick elements fairly in each sub-enum. The given enum
+      must be finite (not its elements, though). *)
 
 val persistent : 'a generator -> 'a t
   (** Store content of the generator in memory, to be able to iterate on it