diff --git a/src/tgba/tgba.hh b/src/tgba/tgba.hh
index 69b2f55e2..ae7359b99 100644
--- a/src/tgba/tgba.hh
+++ b/src/tgba/tgba.hh
@@ -658,7 +658,6 @@ namespace spot
     {
       set_num_sets_(num);
       acc_.set_acceptance(c);
-      prop_single_acc_set(!acc_.uses_fin_acceptance() && num == 1);
       if (num == 0)
 	prop_state_based_acc();
     }
@@ -668,7 +667,6 @@ namespace spot
     {
       acc_ = a->acc();
       unsigned num = acc_.num_sets();
-      prop_single_acc_set(!acc_.uses_fin_acceptance() && num == 1);
       if (num == 0)
 	prop_state_based_acc();
     }
@@ -682,7 +680,6 @@ namespace spot
     {
       set_num_sets_(num);
       acc_.set_generalized_buchi();
-      prop_single_acc_set(num == 1);
       if (num == 0)
 	prop_state_based_acc();
     }
@@ -706,7 +703,6 @@ namespace spot
     // holds, but false means the property is unknown.
     struct bprop
     {
-      bool single_acc_set:1;	// A single acceptance set.
       bool state_based_acc:1;	// State-based acceptance.
       bool inherently_weak:1;	// Weak automaton.
       bool deterministic:1;	// Deterministic automaton.
@@ -748,16 +744,6 @@ namespace spot
     }
 #endif
 
-    bool has_single_acc_set() const
-    {
-      return is.single_acc_set;
-    }
-
-    void prop_single_acc_set(bool val = true)
-    {
-      is.single_acc_set = val;
-    }
-
     bool has_state_based_acc() const
     {
       return is.state_based_acc;
@@ -770,7 +756,7 @@ namespace spot
 
     bool is_sba() const
     {
-      return has_state_based_acc() && has_single_acc_set();
+      return has_state_based_acc() && acc().is_buchi();
     }
 
     bool is_inherently_weak() const
@@ -806,14 +792,13 @@ namespace spot
     struct prop_set
     {
       bool state_based;
-      bool single_acc;
       bool inherently_weak;
       bool deterministic;
       bool stutter_inv;
 
       static prop_set all()
       {
-	return { true, true, true, true, true };
+	return { true, true, true, true };
       }
     };
 
@@ -823,8 +808,6 @@ namespace spot
     {
       if (p.state_based)
 	prop_state_based_acc(other->has_state_based_acc());
-      if (p.single_acc)
-	prop_single_acc_set(other->has_single_acc_set());
       if (p.inherently_weak)
 	prop_inherently_weak(other->is_inherently_weak());
       if (p.deterministic)
@@ -837,8 +820,6 @@ namespace spot
     {
       if (!p.state_based)
 	prop_state_based_acc(false);
-      if (!p.single_acc)
-	prop_single_acc_set(false);
       if (!p.inherently_weak)
 	prop_inherently_weak(false);
       if (!p.deterministic)
diff --git a/src/tgbaalgos/complete.cc b/src/tgbaalgos/complete.cc
index 4802ae6e4..c5d56cfbe 100644
--- a/src/tgbaalgos/complete.cc
+++ b/src/tgbaalgos/complete.cc
@@ -106,7 +106,6 @@ namespace spot
   {
     auto res = make_tgba_digraph(aut, {
 					true, // state based
-					true, // single acc
 					true, // inherently_weak
 					true, // deterministic
 					true, // stutter inv.
diff --git a/src/tgbaalgos/degen.cc b/src/tgbaalgos/degen.cc
index 5ebe9dfbc..7a0271171 100644
--- a/src/tgbaalgos/degen.cc
+++ b/src/tgbaalgos/degen.cc
@@ -205,7 +205,7 @@ namespace spot
       if (want_sba)
 	res->prop_state_based_acc();
       // Preserve determinism, weakness, and stutter-invariance
-      res->prop_copy(a, { false, false, true, true, true });
+      res->prop_copy(a, { false, true, true, true });
 
       // Create an order of acceptance conditions.  Each entry in this
       // vector correspond to an acceptance set.  Each index can
@@ -567,7 +567,7 @@ namespace spot
   {
     // If this already a degeneralized digraph, there is nothing we
     // can improve.
-    if (a->has_single_acc_set())
+    if (a->acc().is_buchi())
       return std::const_pointer_cast<tgba_digraph>(a);
 
     return degeneralize_aux<false>(a, use_z_lvl, use_cust_acc_orders,
diff --git a/src/tgbaalgos/dtgbacomp.cc b/src/tgbaalgos/dtgbacomp.cc
index 1a05bc0fc..2069cd29e 100644
--- a/src/tgbaalgos/dtgbacomp.cc
+++ b/src/tgbaalgos/dtgbacomp.cc
@@ -29,7 +29,6 @@ namespace spot
     // Clone the original automaton.
     auto res = make_tgba_digraph(aut,
 				 { false, // state based
-				   false, // single acc
 				   false, // inherently_weak
 				   false, // deterministic
 				   true,  // stutter inv.
@@ -118,7 +117,6 @@ namespace spot
     // Clone the original automaton.
     auto res = make_tgba_digraph(aut,
 				 { true, // state based
-				   true, // single acc
 				   true, // inherently weak
 				   true, // determinisitic
 				   true,  // stutter inv.
diff --git a/src/tgbaalgos/mask.cc b/src/tgbaalgos/mask.cc
index e431745ac..4218bf04a 100644
--- a/src/tgbaalgos/mask.cc
+++ b/src/tgbaalgos/mask.cc
@@ -26,7 +26,7 @@ namespace spot
   {
     auto res = make_tgba_digraph(in->get_dict());
     res->copy_ap_of(in);
-    res->prop_copy(in, { true, false, true, true, false });
+    res->prop_copy(in, { true, true, true, false });
     unsigned na = in->acc().num_sets();
     unsigned tr = to_remove.count();
     assert(tr <= na);
@@ -54,7 +54,7 @@ namespace spot
 
     auto res = make_tgba_digraph(in->get_dict());
     res->copy_ap_of(in);
-    res->prop_copy(in, { true, true, true, true, false });
+    res->prop_copy(in, { true, true, true, false });
     res->copy_acceptance_of(in);
     transform_copy(in, res, [&](unsigned src,
                                 bdd& cond,
diff --git a/src/tgbaalgos/minimize.cc b/src/tgbaalgos/minimize.cc
index 69d5d7bd4..87903faf1 100644
--- a/src/tgbaalgos/minimize.cc
+++ b/src/tgbaalgos/minimize.cc
@@ -485,7 +485,7 @@ namespace spot
     // final is empty: there is no acceptance condition
     build_state_set(det_a, non_final);
     auto res = minimize_dfa(det_a, final, non_final);
-    res->prop_copy(a, { false, false, false, false, true });
+    res->prop_copy(a, { false, false, false, true });
     res->prop_deterministic();
     res->prop_inherently_weak();
     res->prop_state_based_acc();
@@ -589,7 +589,7 @@ namespace spot
     }
 
     auto res = minimize_dfa(det_a, final, non_final);
-    res->prop_copy(a, { false, false, false, false, true });
+    res->prop_copy(a, { false, false, false, true });
     res->prop_deterministic();
     res->prop_inherently_weak();
     return res;
diff --git a/src/tgbaalgos/remfin.cc b/src/tgbaalgos/remfin.cc
index b391fabee..63edcd59e 100644
--- a/src/tgbaalgos/remfin.cc
+++ b/src/tgbaalgos/remfin.cc
@@ -262,7 +262,7 @@ namespace spot
     unsigned nst = aut->num_states();
     auto res = make_tgba_digraph(aut->get_dict());
     res->copy_ap_of(aut);
-    res->prop_copy(aut, { false, false, false, false, true });
+    res->prop_copy(aut, { false, false, false, true });
     res->new_states(nst);
     res->set_acceptance(aut->acc().num_sets() + extra_sets, new_code);
     res->set_init_state(aut->get_init_state_number());
diff --git a/src/tgbaalgos/sccfilter.cc b/src/tgbaalgos/sccfilter.cc
index cdda763d1..790dc81d9 100644
--- a/src/tgbaalgos/sccfilter.cc
+++ b/src/tgbaalgos/sccfilter.cc
@@ -317,7 +317,7 @@ namespace spot
   scc_filter_states(const const_tgba_digraph_ptr& aut, scc_info* given_si)
   {
     auto res = scc_filter_apply<state_filter<>>(aut, given_si);
-    res->prop_copy(aut, { true, true, true, true, true });
+    res->prop_copy(aut, { true, true, true, true });
     return res;
   }
 
@@ -340,7 +340,6 @@ namespace spot
 		     true,
 		     true,
 		     true,
-		     true,
 		   });
     return res;
   }
@@ -370,7 +369,6 @@ namespace spot
     res->merge_transitions();
     res->prop_copy(aut,
 		   { false,  // state-based acceptance is not preserved
-		     true,
 		     true,
 		     false,	// determinism may not be preserved
 		     false,  	// stutter inv. of suspvars probably altered
diff --git a/src/tgbaalgos/simulation.cc b/src/tgbaalgos/simulation.cc
index 0a538cb4e..4a0c130a8 100644
--- a/src/tgbaalgos/simulation.cc
+++ b/src/tgbaalgos/simulation.cc
@@ -632,7 +632,6 @@ namespace spot
 	delete gb;
 	res->prop_copy(original_,
 		       { false, // state-based acc forced below
-			 false, // single acc set by set_generalized_buchi
 		         true,  // weakness preserved,
 			 false, // determinism checked and set below
 			 true, // stutter inv.
diff --git a/src/tgbaalgos/stutter.cc b/src/tgbaalgos/stutter.cc
index 700fdad65..634938711 100644
--- a/src/tgbaalgos/stutter.cc
+++ b/src/tgbaalgos/stutter.cc
@@ -429,7 +429,6 @@ namespace spot
       }
     if (num_states != a->num_states())
       a->prop_keep({true,	// state_based
-	            true,	// single_acc
 	            false,	// inherently_weak
 	            false,	// deterministic
 	            false,      // stutter inv.
@@ -450,7 +449,6 @@ namespace spot
   closure(tgba_digraph_ptr&& a)
   {
     a->prop_keep({false,	// state_based
-	          true,		// single_acc
 	          false,	// inherently_weak
 	          false,	// deterministic
 	          false,        // stutter inv.
@@ -518,7 +516,7 @@ namespace spot
   tgba_digraph_ptr
   closure(const const_tgba_digraph_ptr& a)
   {
-    return closure(make_tgba_digraph(a, {true, true, true, true, false}));
+    return closure(make_tgba_digraph(a, {true, true, true, false}));
   }
 
   // The stutter check algorithm to use can be overridden via an