diff --git a/spot/tests/acc.cc b/spot/tests/acc.cc
index a32cbb046..f1aa8270e 100644
--- a/spot/tests/acc.cc
+++ b/spot/tests/acc.cc
@@ -91,11 +91,11 @@ int main()
   ac3.set_generalized_buchi();
   std::cout << ac.num_sets() << " + "
 	    << ac2.num_sets() << " = " << ac3.num_sets() << '\n';
-  auto m5 = ac3.join(ac, m2, ac2, m3);
+  auto m5 = m2 | (m3 << ac.num_sets());
   check(ac3, m5);
-  auto m6 = ac3.join(ac, ac.comp(m2 & m3), ac2, m3);
+  auto m6 = ac.comp(m2 & m3) | (m3 << ac.num_sets());
   check(ac3, m6);
-  auto m7 = ac3.join(ac, ac.comp(m2 & m3), ac2, ac2.all_sets());
+  auto m7 = ac.comp(m2 & m3) | (ac.all_sets() << ac.num_sets());
   check(ac3, m7);
 
   const char* comma = "";
diff --git a/spot/twa/acc.hh b/spot/twa/acc.hh
index 97f9f8c93..39cb17420 100644
--- a/spot/twa/acc.hh
+++ b/spot/twa/acc.hh
@@ -167,23 +167,23 @@ namespace spot
 	return id ^ r.id;
       }
 
-      mark_t operator<<(int i) const
+      mark_t operator<<(unsigned i) const
       {
 	return id << i;
       }
 
-      mark_t& operator<<=(int i)
+      mark_t& operator<<=(unsigned i)
       {
 	id <<= i;
 	return *this;
       }
 
-      mark_t operator>>(int i) const
+      mark_t operator>>(unsigned i) const
       {
 	return id >> i;
       }
 
-      mark_t& operator>>=(int i)
+      mark_t& operator>>=(unsigned i)
       {
 	id >>= i;
 	return *this;
@@ -1072,15 +1072,8 @@ namespace spot
 
     mark_t mark(unsigned u) const
     {
-      return mark_(u);
-    }
-
-    mark_t join(const acc_cond& la, mark_t lm,
-		const acc_cond& ra, mark_t rm) const
-    {
-      assert(la.num_sets() + ra.num_sets() == num_sets());
-      (void)ra;
-      return lm.id | (rm.id << la.num_sets());
+      assert(u < num_sets());
+      return 1U << u;
     }
 
     mark_t comp(mark_t l) const
@@ -1151,12 +1144,6 @@ namespace spot
     }
 
   protected:
-    mark_t::value_t mark_(unsigned u) const
-    {
-      assert(u < num_sets());
-      return 1U << u;
-    }
-
     mark_t::value_t all_sets_() const
     {
       if (num_ == 0)
diff --git a/spot/twa/twaproduct.cc b/spot/twa/twaproduct.cc
index 4f3f8da46..5bf1018b2 100644
--- a/spot/twa/twaproduct.cc
+++ b/spot/twa/twaproduct.cc
@@ -203,12 +203,8 @@ namespace spot
 
       acc_cond::mark_t acc() const
       {
-	return
-	  prod_->acc().join(prod_->left_acc(),
-			    left_->acc(),
-			    prod_->right_acc(),
-			    right_->acc());
-       }
+	return left_->acc() | (right_->acc() << prod_->left_acc().num_sets());
+      }
 
     protected:
       bdd current_cond_;
diff --git a/spot/twaalgos/compsusp.cc b/spot/twaalgos/compsusp.cc
index f530fbf35..3edd37f43 100644
--- a/spot/twaalgos/compsusp.cc
+++ b/spot/twaalgos/compsusp.cc
@@ -168,11 +168,10 @@ namespace spot
       dict->register_all_variables_of(right, res);
       dict->unregister_variable(bdd_var(v), res);
 
-      const acc_cond& la = left->acc();
-      const acc_cond& ra = right->acc();
-      res->set_generalized_buchi(la.num_sets() + ra.num_sets());
+      unsigned lsets = left->num_sets();
+      res->set_generalized_buchi(lsets + right->num_sets());
 
-      acc_cond::mark_t radd = ra.all_sets();
+      acc_cond::mark_t radd = right->acc().all_sets();
 
       pair_map seen;
       pair_queue todo;
@@ -246,9 +245,7 @@ namespace spot
 		      todo.push_back(d);
 		    }
 
-		  acc_cond::mark_t a =
-		    res->acc().join(la, li->acc(),
-				    ra, racc);
+		  acc_cond::mark_t a = li->acc() | (racc << lsets);
 		  res->new_edge(src, dest, bdd_exist(cond, v), a);
 
 		  if (ri)
diff --git a/spot/twaalgos/product.cc b/spot/twaalgos/product.cc
index 738ba9347..b0a37bc46 100644
--- a/spot/twaalgos/product.cc
+++ b/spot/twaalgos/product.cc
@@ -96,8 +96,7 @@ namespace spot
 		  continue;
 		auto dst = new_state(l.dst, r.dst);
 		res->new_edge(top.second, dst, cond,
-			      res->acc().join(left->acc(), l.acc,
-					      right->acc(), r.acc));
+			      l.acc | (r.acc << left_num));
 		// If right is deterministic, we can abort immediately!
 	      }
 	}
diff --git a/spot/twaalgos/remfin.cc b/spot/twaalgos/remfin.cc
index 27d47e90c..a9d5ac824 100644
--- a/spot/twaalgos/remfin.cc
+++ b/spot/twaalgos/remfin.cc
@@ -63,7 +63,7 @@ namespace spot
       // Let f=[F₁,F₂,...] and i=[I₁,I₂,...] be bitvectors where bit
       // Fᵢ (resp. Iᵢ) indicates that Fᵢ (resp. Iᵢ) has been visited
       // in the SCC.
-      acc_cond::mark_t f = (sets << 1) & inf_pairs;
+      acc_cond::mark_t f = (sets << 1U) & inf_pairs;
       acc_cond::mark_t i = sets & inf_pairs;
       // If we have i&!f = [0,0,...] that means that the cycle formed
       // by the entire SCC is not accepting.  However that does not
@@ -168,7 +168,7 @@ namespace spot
       acc_cond::mark_t inf;
       std::tie(inf, fin) = aut->get_acceptance().used_inf_fin_sets();
       assert(inf == (inf_pairs | inf_alone));
-      assert(fin == ((inf_pairs >> 1) | fin_alone));
+      assert(fin == ((inf_pairs >> 1U) | fin_alone));
 #endif
       ba_final_states.resize(aut->num_states(), false);
       ba_type = true;		// until proven otherwise
@@ -254,7 +254,7 @@ namespace spot
 	      // and for all Inf sets that have no matching Fin
 	      // sets in this SCC.
 	      acc_cond::mark_t sccsets = si.acc(n);
-	      acc_cond::mark_t f = (sccsets << 1) & inf_pairs;
+	      acc_cond::mark_t f = (sccsets << 1U) & inf_pairs;
 	      acc_cond::mark_t i = sccsets & (inf_pairs | inf_alone);
 	      i -= f;
 	      for (auto s: states)
@@ -264,7 +264,7 @@ namespace spot
 		    res->new_acc_edge(s, t.dst, t.cond, acc);
 		}
 
-	      auto rem = sccsets & ((inf_pairs >> 1) | fin_alone);
+	      auto rem = sccsets & ((inf_pairs >> 1U) | fin_alone);
 	      assert(rem != 0U);
 	      auto sets = rem.sets();
 
@@ -347,7 +347,7 @@ namespace spot
 		  o2 != acc_cond::acc_op::Inf ||
 		  m1.count() != 1 ||
 		  m2.count() != 1 ||
-		  m2 != (m1 << 1))
+		  m2 != (m1 << 1U))
 		return nullptr;
 	      inf_pairs |= m2;
 	    }
diff --git a/spot/twaalgos/totgba.cc b/spot/twaalgos/totgba.cc
index 025c2e532..91e45a01a 100644
--- a/spot/twaalgos/totgba.cc
+++ b/spot/twaalgos/totgba.cc
@@ -126,7 +126,7 @@ namespace spot
     acc_cond::mark_t inf;
     acc_cond::mark_t fin;
     std::tie(inf, fin) = in->get_acceptance().used_inf_fin_sets();
-    assert((inf >> 1) == fin);
+    assert((inf >> 1U) == fin);
 
     scc_info si(in);
 
@@ -139,8 +139,8 @@ namespace spot
 	auto acc = si.acc_sets_of(s); // {0,1,2,3,4,6,7,9}
 	auto acc_fin = acc & fin;     // {0,  2,  4,6}
 	auto acc_inf = acc & inf;     // {  1,  3,    7,9}
-	auto fin_wo_inf = acc_fin - (acc_inf >> 1); // {4}
-	auto inf_wo_fin = acc_inf - (acc_fin << 1); // {9}
+	auto fin_wo_inf = acc_fin - (acc_inf >> 1U); // {4}
+	auto inf_wo_fin = acc_inf - (acc_fin << 1U); // {9}
 	sccfi.emplace_back(fin_wo_inf, inf_wo_fin, acc_fin == 0U);
       }
 
@@ -199,7 +199,7 @@ namespace spot
 		  continue;
 		// For any Fin set we see, we want to see the
 		// corresponding Inf set.
-		pend |= (t.acc & fin) << 1;
+		pend |= (t.acc & fin) << 1U;
 		pend -= t.acc & inf;
 		// Label this transition with all non-pending
 		// inf sets.  The strip will shift everything
@@ -212,7 +212,7 @@ namespace spot
 		    auto a = in->state_acc_sets(t.dst);
 		    if (a & scc_fin_wo_inf)
 		      continue;
-		    pend |= (a & fin) << 1;
+		    pend |= (a & fin) << 1U;
 		    pend -= a & inf;
 		  }
 		pend |= scc_inf_wo_fin;
@@ -250,7 +250,7 @@ namespace spot
 		    auto a = in->state_acc_sets(t.dst);
 		    if (a & scc_fin_wo_inf)
 		      continue;
-		    pend = (a & fin) << 1;
+		    pend = (a & fin) << 1U;
 		    pend -= a & inf;
 		  }
 		st2gba_state d(t.dst, pend | scc_inf_wo_fin);