diff --git a/spot/twacube_algos/convert.cc b/spot/twacube_algos/convert.cc
index ba84ce46e..e49194b90 100644
--- a/spot/twacube_algos/convert.cc
+++ b/spot/twacube_algos/convert.cc
@@ -134,14 +134,15 @@ namespace spot
   }
 
   spot::twa_graph_ptr
-  twacube_to_twa(spot::twacube_ptr twacube)
+  twacube_to_twa(spot::twacube_ptr twacube, spot::bdd_dict_ptr d)
   {
     // Grab necessary variables
     auto& theg = twacube->get_graph();
     spot::cubeset cs = twacube->get_cubeset();
 
     // Build the resulting graph
-    auto d = spot::make_bdd_dict();
+    if (d == nullptr)
+      d = spot::make_bdd_dict();
     auto res = make_twa_graph(d);
 
     // Fix the acceptance of the resulting automaton
diff --git a/spot/twacube_algos/convert.hh b/spot/twacube_algos/convert.hh
index bdcfc7155..f21aaec3f 100644
--- a/spot/twacube_algos/convert.hh
+++ b/spot/twacube_algos/convert.hh
@@ -50,9 +50,12 @@ namespace spot
   SPOT_API twacube_ptr
   twa_to_twacube(spot::const_twa_graph_ptr aut);
 
-  /// \brief Convert a twacube into a twa
+  /// \brief Convert a twacube into a twa.
+  /// When \d is specified, the BDD_dict in parameter is used rather than
+  /// creating a new one.
   SPOT_API spot::twa_graph_ptr
-  twacube_to_twa(spot::twacube_ptr twacube);
+  twacube_to_twa(spot::twacube_ptr twacube,
+                 spot::bdd_dict_ptr d = nullptr);
 
   /// \brief Check wether a twacube and a twa are equivalent
   SPOT_API bool are_equivalent(const spot::twacube_ptr twacube,
diff --git a/tests/core/twacube.cc b/tests/core/twacube.cc
index 08333cc4e..31eeaed69 100644
--- a/tests/core/twacube.cc
+++ b/tests/core/twacube.cc
@@ -44,8 +44,10 @@ static void checkit(std::string f_str)
   auto propcube = spot::twa_to_twacube(prop);
   assert(spot::are_equivalent(propcube, prop));
 
-  auto propcubeback = spot::twacube_to_twa(propcube);
+  auto propcubeback = spot::twacube_to_twa(propcube, dict);
   assert(spot::are_equivalent(propcube, propcubeback));
+
+  assert(spot::are_equivalent(prop, propcubeback));
 }
 
 int main()