diff --git a/src/twa/twa.hh b/src/twa/twa.hh
index 18492cb94..1d5956e25 100644
--- a/src/twa/twa.hh
+++ b/src/twa/twa.hh
@@ -658,6 +658,11 @@ namespace spot
     }
 
   public:
+    unsigned num_sets() const
+    {
+      return acc_.num_sets();
+    }
+
     const acc_cond::acc_code& get_acceptance() const
     {
       return acc_.get_acceptance();
diff --git a/src/twa/twagraph.hh b/src/twa/twagraph.hh
index 5ad66f5c4..ed3d43a49 100644
--- a/src/twa/twagraph.hh
+++ b/src/twa/twagraph.hh
@@ -438,7 +438,7 @@ namespace spot
 
     acc_cond::mark_t state_acc_sets(unsigned s) const
     {
-      assert(has_state_based_acc() || acc_.num_sets() == 0);
+      assert(has_state_based_acc() || num_sets() == 0);
       for (auto& t: g_.out(s))
 	// Stop at the first transition, since the remaining should be
 	// labeled identically.
@@ -448,7 +448,7 @@ namespace spot
 
     bool state_is_accepting(unsigned s) const
     {
-      assert(has_state_based_acc() || acc_.num_sets() == 0);
+      assert(has_state_based_acc() || num_sets() == 0);
       for (auto& t: g_.out(s))
 	// Stop at the first transition, since the remaining should be
 	// labeled identically.
@@ -465,7 +465,7 @@ namespace spot
     {
       if (num_states() != aut.num_states() ||
           num_transitions() != aut.num_transitions() ||
-          acc().num_sets() != aut.acc().num_sets())
+          num_sets() != aut.num_sets())
         return false;
       auto& trans1 = transition_vector();
       auto& trans2 = aut.transition_vector();
diff --git a/src/twa/twaproduct.cc b/src/twa/twaproduct.cc
index 5de3c44ef..949a2465f 100644
--- a/src/twa/twaproduct.cc
+++ b/src/twa/twaproduct.cc
@@ -310,12 +310,12 @@ namespace spot
     d->register_all_propositions_of(&left_, this);
     d->register_all_propositions_of(&right_, this);
 
-    assert(acc_.num_sets() == 0);
-    auto left_num = left->acc().num_sets();
+    assert(num_sets() == 0);
+    auto left_num = left->num_sets();
     auto right_acc = right->get_acceptance();
     right_acc.shift_left(left_num);
     right_acc.append_and(left->get_acceptance());
-    set_acceptance(left_num + right->acc().num_sets(), right_acc);
+    set_acceptance(left_num + right->num_sets(), right_acc);
   }
 
   twa_product::~twa_product()
diff --git a/src/twa/twaproxy.cc b/src/twa/twaproxy.cc
index d24001156..21f2ae4ca 100644
--- a/src/twa/twaproxy.cc
+++ b/src/twa/twaproxy.cc
@@ -25,7 +25,7 @@ namespace spot
     : twa(original->get_dict()), original_(original)
   {
     get_dict()->register_all_variables_of(original, this);
-    acc_.add_sets(original->acc().num_sets());
+    acc_.add_sets(original->num_sets());
   }
 
   twa_proxy::~twa_proxy()
diff --git a/src/twaalgos/degen.cc b/src/twaalgos/degen.cc
index 518d82ac2..d4e5b2371 100644
--- a/src/twaalgos/degen.cc
+++ b/src/twaalgos/degen.cc
@@ -226,7 +226,7 @@ namespace spot
 	// used in the automaton.  (This surprising fact is probably
 	// related to the order in which we declare the BDD variables
 	// during the translation.)
-	unsigned n = a->acc().num_sets();
+	unsigned n = a->num_sets();
 	for (unsigned i = n; i > 0; --i)
 	  order.push_back(i - 1);
       }
diff --git a/src/twaalgos/dot.cc b/src/twaalgos/dot.cc
index 15e2ee4bf..8f4ee374c 100644
--- a/src/twaalgos/dot.cc
+++ b/src/twaalgos/dot.cc
@@ -277,7 +277,7 @@ namespace spot
 	if (opt_html_labels_)
 	  std::tie(inf_sets_, fin_sets_) =
 	    aut_->get_acceptance().used_inf_fin_sets();
-	if (opt_bullet && aut_->acc().num_sets() <= MAX_BULLET)
+	if (opt_bullet && aut_->num_sets() <= MAX_BULLET)
 	  opt_all_bullets = true;
 	os_ << "digraph G {\n";
 	if (opt_horizontal_)
@@ -366,7 +366,7 @@ namespace spot
       {
 	if (mark_states_ &&
 	    ((opt_bullet && !opt_bullet_but_buchi)
-	     || aut_->acc().num_sets() != 1))
+	     || aut_->num_sets() != 1))
 	  {
 	    acc_cond::mark_t acc = 0U;
 	    for (auto& t: aut_->out(s))
diff --git a/src/twaalgos/dtgbacomp.cc b/src/twaalgos/dtgbacomp.cc
index 6555804f4..afe41dfca 100644
--- a/src/twaalgos/dtgbacomp.cc
+++ b/src/twaalgos/dtgbacomp.cc
@@ -174,7 +174,7 @@ namespace spot
 	// Simply complete the automaton, and complement its
 	// acceptance.
 	auto res = cleanup_acceptance_here(tgba_complete(aut));
-	res->set_acceptance(res->acc().num_sets(),
+	res->set_acceptance(res->num_sets(),
 			    res->get_acceptance().complement());
 	return res;
       }
diff --git a/src/twaalgos/dtgbasat.cc b/src/twaalgos/dtgbasat.cc
index 67a930164..81096dea9 100644
--- a/src/twaalgos/dtgbasat.cc
+++ b/src/twaalgos/dtgbasat.cc
@@ -472,7 +472,7 @@ namespace spot
 	}
 
       d.all_ref_acc.push_back(0U);
-      unsigned ref_nacc = aut->acc().num_sets();
+      unsigned ref_nacc = aut->num_sets();
       for (unsigned n = 0; n < ref_nacc; ++n)
 	{
 	  auto c = aut->acc().mark(n);
@@ -1233,7 +1233,7 @@ namespace spot
     // Assume we are going to use the input automaton acceptance...
     bool user_supplied_acc = false;
     acc_cond::acc_code target_acc = a->get_acceptance();
-    int nacc = a->acc().num_sets();
+    int nacc = a->num_sets();
 
     if (accstr == "same")
       accstr.clear();
diff --git a/src/twaalgos/gv04.cc b/src/twaalgos/gv04.cc
index b16f0d037..6c394b1b1 100644
--- a/src/twaalgos/gv04.cc
+++ b/src/twaalgos/gv04.cc
@@ -70,7 +70,7 @@ namespace spot
       gv04(const const_twa_ptr& a, option_map o)
 	: emptiness_check(a, o)
       {
-	assert(a->acc().num_sets() <= 1);
+	assert(a->num_sets() <= 1);
       }
 
       ~gv04()
@@ -383,7 +383,7 @@ namespace spot
 
 	  const state* bfs_start = data.stack[scc_root].s;
 	  const state* bfs_end = bfs_start;
-	  if (a_->acc().num_sets() > 0)
+	  if (a_->num_sets() > 0)
 	    {
 	      first_bfs b1(this, scc_root);
 	      bfs_start = b1.search(bfs_start, res->cycle);
diff --git a/src/twaalgos/hoa.cc b/src/twaalgos/hoa.cc
index b03b0c722..39d511563 100644
--- a/src/twaalgos/hoa.cc
+++ b/src/twaalgos/hoa.cc
@@ -97,7 +97,7 @@ namespace spot
 	bool complete = true;
 	bool state_acc = true;
 	bool nodeadend = true;
-	bool colored = aut->acc().num_sets() >= 1;
+	bool colored = aut->num_sets() >= 1;
 	for (unsigned src = 0; src < ns; ++src)
 	  {
 	    bdd sum = bddfalse;
@@ -296,7 +296,7 @@ namespace spot
       }
     os << nl;
 
-    unsigned num_acc = aut->acc().num_sets();
+    unsigned num_acc = aut->num_sets();
     acc_cond::acc_code acc_c = aut->acc().get_acceptance();
     if (aut->acc().is_generalized_buchi())
       {
diff --git a/src/twaalgos/lbtt.cc b/src/twaalgos/lbtt.cc
index 1366ce8f5..9eb069c2b 100644
--- a/src/twaalgos/lbtt.cc
+++ b/src/twaalgos/lbtt.cc
@@ -115,9 +115,9 @@ namespace spot
       {
 	os_ << seen.size() << ' ';
 	if (sba_format_)
-	  os_ << aut_->acc().num_sets();
+	  os_ << aut_->num_sets();
 	else
-	  os_ << aut_->acc().num_sets() << 't';
+	  os_ << aut_->num_sets() << 't';
 	os_ << '\n' << body_.str() << "-1" << std::endl;
       }
 
diff --git a/src/twaalgos/magic.cc b/src/twaalgos/magic.cc
index 5d6555b4a..0e4981dd2 100644
--- a/src/twaalgos/magic.cc
+++ b/src/twaalgos/magic.cc
@@ -59,7 +59,7 @@ namespace spot
         : emptiness_check(a, o),
           h(size)
       {
-        assert(a->acc().num_sets() <= 1);
+        assert(a->num_sets() <= 1);
       }
 
       virtual ~magic_search_()
diff --git a/src/twaalgos/mask.cc b/src/twaalgos/mask.cc
index eb3675728..7fa799a97 100644
--- a/src/twaalgos/mask.cc
+++ b/src/twaalgos/mask.cc
@@ -27,7 +27,7 @@ namespace spot
     auto res = make_twa_graph(in->get_dict());
     res->copy_ap_of(in);
     res->prop_copy(in, { true, true, true, false });
-    unsigned na = in->acc().num_sets();
+    unsigned na = in->num_sets();
     unsigned tr = to_remove.count();
     assert(tr <= na);
     res->set_acceptance(na - tr,
diff --git a/src/twaalgos/ndfs_result.hxx b/src/twaalgos/ndfs_result.hxx
index 315f398e0..4c272a826 100644
--- a/src/twaalgos/ndfs_result.hxx
+++ b/src/twaalgos/ndfs_result.hxx
@@ -119,7 +119,7 @@ namespace spot
       start = stb.front().s->clone();
       if (!str.empty())
         {
-          if (a_->acc().num_sets() == 0)
+          if (a_->num_sets() == 0)
             {
               // take arbitrarily the last transition on the red stack
               stack_type::const_iterator i, j;
diff --git a/src/twaalgos/postproc.cc b/src/twaalgos/postproc.cc
index ff96d3be1..5e8047ee0 100644
--- a/src/twaalgos/postproc.cc
+++ b/src/twaalgos/postproc.cc
@@ -41,7 +41,7 @@ namespace spot
     static twa_graph_ptr
     ensure_ba(twa_graph_ptr& a)
     {
-      if (a->acc().num_sets() == 0)
+      if (a->num_sets() == 0)
 	{
 	  auto m = a->set_buchi();
 	  for (auto& t: a->transitions())
@@ -153,7 +153,7 @@ namespace spot
       if (type_ == Generic
 	  || type_ == TGBA
 	  || (type_ == BA && a->is_sba())
-	  || (type_ == Monitor && a->acc().num_sets() == 0))
+	  || (type_ == Monitor && a->num_sets() == 0))
 	{
 	  if (COMP_)
 	    a = tgba_complete(a);
@@ -171,7 +171,7 @@ namespace spot
     if (type_ == BA || SBACC_)
       state_based_ = true;
 
-    int original_acc = a->acc().num_sets();
+    int original_acc = a->num_sets();
 
     // Remove useless SCCs.
     if (type_ == Monitor)
@@ -301,7 +301,7 @@ namespace spot
 	if (PREF_ == Deterministic
 	    && f
 	    && f->is_syntactic_recurrence()
-	    && sim->acc().num_sets() > 1)
+	    && sim->num_sets() > 1)
 	  tmpd = degeneralize_tba(sim);
 
 	auto in = tmpd ? tmpd : sim;
@@ -370,7 +370,7 @@ namespace spot
 	    // because the input TBA might be smaller.
 	    if (state_based_)
 	      in = degeneralize(dba);
-	    else if (dba->acc().num_sets() != 1)
+	    else if (dba->num_sets() != 1)
 	      in = degeneralize_tba(dba);
 	    else
 	      in = dba;
@@ -423,7 +423,7 @@ namespace spot
     // Degeneralize the dba resulting from tba-determinization or
     // sat-minimization (which is a TBA) if requested and needed.
     if (dba && !dba_is_wdba && type_ == BA
-	&& !(dba_is_minimal && state_based_ && dba->acc().num_sets() == 1))
+	&& !(dba_is_minimal && state_based_ && dba->num_sets() == 1))
       dba = degeneralize(dba);
 
     if (dba && sim)
diff --git a/src/twaalgos/powerset.cc b/src/twaalgos/powerset.cc
index 52daabbe6..ea66f3e84 100644
--- a/src/twaalgos/powerset.cc
+++ b/src/twaalgos/powerset.cc
@@ -410,7 +410,7 @@ namespace spot
   {
     if (f == 0 && neg_aut == 0)
       return 0;
-    if (aut->acc().num_sets() > 1)
+    if (aut->num_sets() > 1)
       return 0;
 
     auto det = tba_determinize(aut, threshold_states, threshold_cycles);
diff --git a/src/twaalgos/product.cc b/src/twaalgos/product.cc
index d21d91f24..b4e1b6a01 100644
--- a/src/twaalgos/product.cc
+++ b/src/twaalgos/product.cc
@@ -52,11 +52,11 @@ namespace spot
     auto res = make_twa_graph(left->get_dict());
     res->copy_ap_of(left);
     res->copy_ap_of(right);
-    auto left_num = left->acc().num_sets();
+    auto left_num = left->num_sets();
     auto right_acc = right->get_acceptance();
     right_acc.shift_left(left_num);
     right_acc.append_and(left->get_acceptance());
-    res->set_acceptance(left_num + right->acc().num_sets(), right_acc);
+    res->set_acceptance(left_num + right->num_sets(), right_acc);
 
     auto v = new product_states;
     res->set_named_prop("product-states", v);
diff --git a/src/twaalgos/remfin.cc b/src/twaalgos/remfin.cc
index fe660399a..d84b5b9d9 100644
--- a/src/twaalgos/remfin.cc
+++ b/src/twaalgos/remfin.cc
@@ -264,7 +264,7 @@ namespace spot
     res->copy_ap_of(aut);
     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_acceptance(aut->num_sets() + extra_sets, new_code);
     res->set_init_state(aut->get_init_state_number());
 
     unsigned nscc = si.scc_count();
diff --git a/src/twaalgos/se05.cc b/src/twaalgos/se05.cc
index 9659c2e60..ec16d4ffa 100644
--- a/src/twaalgos/se05.cc
+++ b/src/twaalgos/se05.cc
@@ -59,7 +59,7 @@ namespace spot
         : emptiness_check(a, o),
           h(size)
       {
-        assert(a->acc().num_sets() <= 1);
+        assert(a->num_sets() <= 1);
       }
 
       virtual ~se05_search()
diff --git a/src/twaalgos/simulation.cc b/src/twaalgos/simulation.cc
index 42bf1f3e1..1a04f5147 100644
--- a/src/twaalgos/simulation.cc
+++ b/src/twaalgos/simulation.cc
@@ -258,7 +258,7 @@ namespace spot
 	unsigned set_num = a_->get_dict()
 	  ->register_anonymous_variables(size_a_ + 1, this);
 
-	unsigned n_acc = a_->acc().num_sets();
+	unsigned n_acc = a_->num_sets();
 	acc_vars = a_->get_dict()
 	  ->register_anonymous_variables(n_acc, this);
 
diff --git a/src/twaalgos/stats.cc b/src/twaalgos/stats.cc
index 12d211676..f516f3937 100644
--- a/src/twaalgos/stats.cc
+++ b/src/twaalgos/stats.cc
@@ -183,7 +183,7 @@ namespace spot
       }
 
     if (has('a'))
-      acc_ = aut->acc().num_sets();
+      acc_ = aut->num_sets();
 
     if (has('c') || has('S'))
       scc_ = scc_info(aut).scc_count();
diff --git a/src/twaalgos/stutter.cc b/src/twaalgos/stutter.cc
index 985f55196..e6179e620 100644
--- a/src/twaalgos/stutter.cc
+++ b/src/twaalgos/stutter.cc
@@ -213,7 +213,7 @@ namespace spot
       {
 	get_dict()->register_all_propositions_of(&a_, this);
 	assert(acc_.num_sets() == 0);
-	acc_.add_sets(a_->acc().num_sets());
+	acc_.add_sets(a_->num_sets());
 	acc_.set_generalized_buchi();
       }
 
diff --git a/src/twaalgos/tau03.cc b/src/twaalgos/tau03.cc
index d499d2227..531e41793 100644
--- a/src/twaalgos/tau03.cc
+++ b/src/twaalgos/tau03.cc
@@ -58,7 +58,7 @@ namespace spot
         : emptiness_check(a, o),
           h(size)
       {
-        assert(a->acc().num_sets() > 0);
+        assert(a->num_sets() > 0);
       }
 
       virtual ~tau03_search()
diff --git a/src/twaalgos/tau03opt.cc b/src/twaalgos/tau03opt.cc
index a6187e11e..14f687327 100644
--- a/src/twaalgos/tau03opt.cc
+++ b/src/twaalgos/tau03opt.cc
@@ -159,7 +159,7 @@ namespace spot
 	  return acc;
 	// FIXME: This should be improved.
 	std::vector<unsigned> res;
-	unsigned max = a_->acc().num_sets();
+	unsigned max = a_->num_sets();
 	for (unsigned n = 0; n < max && a_->acc().has(acc, n); ++n)
 	  res.push_back(n);
 	return a_->acc().marks(res.begin(), res.end());
diff --git a/src/twaalgos/totgba.cc b/src/twaalgos/totgba.cc
index 8bf320b94..2f1e412b3 100644
--- a/src/twaalgos/totgba.cc
+++ b/src/twaalgos/totgba.cc
@@ -70,7 +70,7 @@ namespace spot
     if (cnf.empty() ||
 	(cnf.size() == 2 && cnf.back().op == acc_cond::acc_op::Inf))
       {
-	res->set_acceptance(res->acc().num_sets(), cnf);
+	res->set_acceptance(res->num_sets(), cnf);
 	cleanup_acceptance_here(res);
 	return res;
       }