diff --git a/src/tgbaalgos/mask.cc b/src/tgbaalgos/mask.cc
index a769f2d3a..9a82a364e 100644
--- a/src/tgbaalgos/mask.cc
+++ b/src/tgbaalgos/mask.cc
@@ -32,15 +32,16 @@ namespace spot
     unsigned tr = to_remove.count();
     assert(tr <= na);
     res->set_acceptance_conditions(na - tr);
-    transform_mask(in, res, [&](bdd& cond,
-				acc_cond::mark_t& acc,
-				unsigned)
-		   {
-		     if (acc & to_remove)
-		       cond = bddfalse;
-		     else
-		       acc = inacc.strip(acc, to_remove);
-		   });
+    transform_accessible(in, res, [&](unsigned,
+                                      bdd& cond,
+                                      acc_cond::mark_t& acc,
+                                      unsigned)
+                         {
+                           if (acc & to_remove)
+                             cond = bddfalse;
+                           else
+                             acc = inacc.strip(acc, to_remove);
+                         });
     return res;
   }
 
@@ -55,11 +56,12 @@ namespace spot
     res->copy_ap_of(in);
     res->prop_copy(in, { true, true, true, true });
     res->copy_acceptance_conditions_of(in);
-    transform_mask(in, res, [&](bdd& cond,
-				acc_cond::mark_t&,
-				unsigned dst)
+    transform_copy(in, res, [&](unsigned src,
+                                bdd& cond,
+                                acc_cond::mark_t&,
+                                unsigned dst)
 		   {
-		     if (!to_keep[dst])
+		     if (!to_keep[src] || !to_keep[dst])
 		       cond = bddfalse;
 		   }, init);
     return res;
diff --git a/src/tgbaalgos/mask.hh b/src/tgbaalgos/mask.hh
index 4e9eb42a0..f02ca0d9c 100644
--- a/src/tgbaalgos/mask.hh
+++ b/src/tgbaalgos/mask.hh
@@ -28,9 +28,10 @@ namespace spot
   ///
   /// Copy the transition of the automaton \a old, into the automaton
   /// \a cpy, creating new states at the same time.  The argument \a
-  /// trans should behave as a fonction with the following prototype:
+  /// trans should behave as a function with the following prototype:
   /// <code>
-  ///   void (*trans) (bdd& cond, acc_cond::mark_t& acc, unsigned dst)
+  ///   void (*trans) (unsigned srcbdd& cond, acc_cond::mark_t& acc,
+  ///   unsigned dst)
   /// </code>
   /// It can modify either the condition or the acceptance sets of
   /// the transitions.  Set the condition to bddfalse to remove it
@@ -39,9 +40,9 @@ namespace spot
   /// \param init The optional new initial state.
 
   template<typename Trans>
-  void transform_mask(const const_tgba_digraph_ptr& old,
-		      tgba_digraph_ptr& cpy,
-		      Trans trans, unsigned int init)
+  void transform_accessible(const const_tgba_digraph_ptr& old,
+                            tgba_digraph_ptr& cpy,
+                            Trans trans, unsigned int init)
   {
     std::vector<unsigned> todo;
     std::vector<unsigned> seen(old->num_states(), -1U);
@@ -72,7 +73,7 @@ namespace spot
 	  {
 	    bdd cond = t.cond;
 	    acc_cond::mark_t acc = t.acc;
-	    trans(cond, acc, t.dst);
+	    trans(t.src, cond, acc, t.dst);
 
 	    if (cond != bddfalse)
 	      cpy->new_transition(new_src,
@@ -82,12 +83,55 @@ namespace spot
       }
   }
 
+  /// \brief Copy an automaton and update each transitions.
+  ///
+  /// Copy the states of the automaton \a old, into the automaton
+  /// \a cpy. Each state in \a cpy will have the same id as the ones in \a old.
+  /// The argument \a trans
+  /// should behave as a function with the following prototype:
+  /// <code>
+  ///   void (*trans) (unsigned srcbdd& cond, acc_cond::mark_t& acc,
+  ///   unsigned dst)
+  /// </code>
+  /// It can modify either the condition or the acceptance sets of
+  /// the transitions.  Set the condition to bddfalse to remove it.  Note that
+  /// all transtions will be processed.
+  /// \param init The optional new initial state.
   template<typename Trans>
-  void transform_mask(const const_tgba_digraph_ptr& old,
-		      tgba_digraph_ptr& cpy,
-		      Trans trans)
+  void transform_copy(const const_tgba_digraph_ptr& old,
+                      tgba_digraph_ptr& cpy,
+                      Trans trans, unsigned int init)
   {
-    transform_mask(old, cpy, trans, old->get_init_state_number());
+    // Each state in cpy corresponds to a unique state in old.
+    cpy->new_states(old->num_states());
+    cpy->set_init_state(init);
+
+    for (auto& t: old->transitions())
+      {
+        bdd cond = t.cond;
+        acc_cond::mark_t acc = t.acc;
+        trans(t.src, cond, acc, t.dst);
+        // Having the same number of states should assure that state ids are
+        // equivilent in old and cpy.
+        assert(t.src < cpy->num_states() && t.dst < cpy->num_states());
+        if (cond != bddfalse)
+          cpy->new_transition(t.src, t.dst, cond, acc);
+      }
+  }
+
+  template<typename Trans>
+  void transform_accessible(const const_tgba_digraph_ptr& old,
+                            tgba_digraph_ptr& cpy,
+                            Trans trans)
+  {
+    transform_accessible(old, cpy, trans, old->get_init_state_number());
+  }
+  template<typename Trans>
+  void transform_copy(const const_tgba_digraph_ptr& old,
+                      tgba_digraph_ptr& cpy,
+                      Trans trans)
+  {
+    transform_copy(old, cpy, trans, old->get_init_state_number());
   }
 
   /// \brief Remove all transitions that are in some given acceptance sets.
diff --git a/src/tgbatest/maskkeep.test b/src/tgbatest/maskkeep.test
index 3ad825795..a5d966a5c 100755
--- a/src/tgbatest/maskkeep.test
+++ b/src/tgbatest/maskkeep.test
@@ -48,7 +48,7 @@ EOF
 
 cat >expect1 <<EOF
 HOA: v1
-States: 1
+States: 4
 Start: 0
 AP: 0
 acc-name: generalized-Buchi 2
@@ -56,6 +56,25 @@ Acceptance: 2 Inf(0)&Inf(1)
 properties: trans-labels explicit-labels state-acc deterministic
 --BODY--
 State: 0
+State: 1
+State: 2
+State: 3
+--END--
+EOF
+
+cat >expect2 <<EOF
+HOA: v1
+States: 4
+Start: 1
+AP: 0
+acc-name: generalized-Buchi 2
+Acceptance: 2 Inf(0)&Inf(1)
+properties: trans-labels explicit-labels state-acc deterministic
+--BODY--
+State: 0
+State: 1
+State: 2
+State: 3
 --END--
 EOF
 
@@ -63,11 +82,11 @@ run 0 ../../bin/autfilt --keep-states=0 input1 -H >output
 diff output expect1
 
 run 0 ../../bin/autfilt --keep-states=1 input1 -H >output
-diff output expect1
+diff output expect2
 
 cat >expect3 <<EOF
 HOA: v1
-States: 3
+States: 4
 Start: 0
 AP: 2 "a" "b"
 acc-name: generalized-Buchi 2
@@ -81,22 +100,27 @@ State: 1
 [0] 2
 State: 2
 [1] 1
+State: 3
 --END--
 EOF
 
 cat >expect4 <<EOF
 HOA: v1
-States: 2
-Start: 0
+States: 4
+Start: 1
 AP: 2 "a" "b"
 acc-name: generalized-Buchi 2
 Acceptance: 2 Inf(0)&Inf(1)
-properties: trans-labels explicit-labels state-acc deterministic
+properties: trans-labels explicit-labels trans-acc
 --BODY--
 State: 0
-[0] 1
+[0] 1 {0}
+[1] 2 {1}
 State: 1
-[1] 0
+[0] 2
+State: 2
+[1] 1
+State: 3
 --END--
 EOF