diff --git a/src/bin/autfilt.cc b/src/bin/autfilt.cc
index 33d35d632..4da23a865 100644
--- a/src/bin/autfilt.cc
+++ b/src/bin/autfilt.cc
@@ -476,7 +476,7 @@ namespace
       if (opt_merge)
 	aut->merge_transitions();
       if (opt_clean_acc || opt_rem_fin)
-	cleanup_acceptance(aut);
+	cleanup_acceptance_here(aut);
       if (opt_complement_acc)
 	aut->set_acceptance(aut->acc().num_sets(),
 			    aut->get_acceptance().complement());
diff --git a/src/bin/ltlcross.cc b/src/bin/ltlcross.cc
index d4ebef7c4..67e0de9f6 100644
--- a/src/bin/ltlcross.cc
+++ b/src/bin/ltlcross.cc
@@ -1110,7 +1110,7 @@ namespace
 	    {
 #define DO(x, prefix, suffix) if (x[i])					\
 		{							\
-		  cleanup_acceptance(x[i]);				\
+		  cleanup_acceptance_here(x[i]);			\
 		  if (x[i]->acc().uses_fin_acceptance())		\
 		    {							\
 	              auto st = x[i]->num_states();			\
diff --git a/src/tgbaalgos/cleanacc.cc b/src/tgbaalgos/cleanacc.cc
index 5ee8027fc..e6523f53a 100644
--- a/src/tgbaalgos/cleanacc.cc
+++ b/src/tgbaalgos/cleanacc.cc
@@ -21,11 +21,11 @@
 
 namespace spot
 {
-  void cleanup_acceptance(tgba_digraph_ptr& aut)
+  tgba_digraph_ptr cleanup_acceptance_here(tgba_digraph_ptr aut)
   {
     auto& acc = aut->acc();
     if (acc.num_sets() == 0)
-      return;
+      return aut;
 
     auto& c = aut->get_acceptance();
     acc_cond::mark_t used_in_cond = c.used_sets();
@@ -39,7 +39,7 @@ namespace spot
     auto useless = acc.comp(useful);
 
     if (!useless)
-      return;
+      return aut;
 
     // Remove useless marks from the automaton
     for (auto& t: aut->transitions())
@@ -50,7 +50,14 @@ namespace spot
 
     // This may in turn cause even more set to be unused, because of
     // some simplifications, so do it again.
-    return cleanup_acceptance(aut);
+    return cleanup_acceptance_here(aut);
   }
 
+  tgba_digraph_ptr cleanup_acceptance(const_tgba_digraph_ptr aut)
+  {
+    return cleanup_acceptance_here(make_tgba_digraph(aut,
+						     tgba::prop_set::all()));
+  }
+
+
 }
diff --git a/src/tgbaalgos/cleanacc.hh b/src/tgbaalgos/cleanacc.hh
index b52de35aa..148ab8c34 100644
--- a/src/tgbaalgos/cleanacc.hh
+++ b/src/tgbaalgos/cleanacc.hh
@@ -24,6 +24,11 @@
 namespace spot
 {
   /// \brief Remove useless acceptance sets
-  SPOT_API void
-  cleanup_acceptance(tgba_digraph_ptr& aut);
+  /// @{
+  SPOT_API tgba_digraph_ptr
+  cleanup_acceptance_here(tgba_digraph_ptr aut);
+
+  SPOT_API tgba_digraph_ptr
+  cleanup_acceptance(const_tgba_digraph_ptr aut);
+  /// @}
 }
diff --git a/src/tgbaalgos/dtgbacomp.cc b/src/tgbaalgos/dtgbacomp.cc
index 2069cd29e..b4091c705 100644
--- a/src/tgbaalgos/dtgbacomp.cc
+++ b/src/tgbaalgos/dtgbacomp.cc
@@ -173,8 +173,7 @@ namespace spot
       {
 	// Simply complete the automaton, and complement its
 	// acceptance.
-	auto res = tgba_complete(aut);
-	cleanup_acceptance(res);
+	auto res = cleanup_acceptance_here(tgba_complete(aut));
 	res->set_acceptance(res->acc().num_sets(),
 			    res->get_acceptance().complement());
 	return res;
diff --git a/src/tgbaalgos/remfin.cc b/src/tgbaalgos/remfin.cc
index 7619f16fa..088dc53c6 100644
--- a/src/tgbaalgos/remfin.cc
+++ b/src/tgbaalgos/remfin.cc
@@ -333,7 +333,7 @@ namespace spot
       }
     res->purge_dead_states();
     trace << "before cleanup: " << res->get_acceptance() << '\n';
-    cleanup_acceptance(res);
+    cleanup_acceptance_here(res);
     trace << "after cleanup: " << res->get_acceptance() << '\n';
     return res;
   }