diff --git a/src/taalgos/emptinessta.cc b/src/taalgos/emptinessta.cc
index c014d3250..b9c214263 100644
--- a/src/taalgos/emptinessta.cc
+++ b/src/taalgos/emptinessta.cc
@@ -205,9 +205,10 @@ namespace spot
                 (a_->is_hole_state_in_ta_component(curr))
                     && a_->is_livelock_accepting_state(curr);
 
-            //may be Buchi accepting scc or livelock accepting state (contains a TA hole and livelock accepting state)
+            //may be Buchi accepting scc or livelock accepting scc (contains a TA "hole and livelock accepting state")
             scc.top().is_accepting = (a_->is_accepting_state(curr)
-                && !succ->is_stuttering_transition())
+                && (!succ->is_stuttering_transition()
+                    || a_->is_livelock_accepting_state(curr)))
                 || curr_is_livelock_hole_state_in_ta_component;
 
             bool is_stuttering_transition = succ->is_stuttering_transition();
diff --git a/src/taalgos/sba2ta.cc b/src/taalgos/sba2ta.cc
index 8f5138467..64ccaa646 100644
--- a/src/taalgos/sba2ta.cc
+++ b/src/taalgos/sba2ta.cc
@@ -140,14 +140,8 @@ namespace spot
             new state_ta_explicit(ta->get_tgba()->get_init_state(), bddfalse,
                 false, false, true, 0, true);
 
-        state_ta_explicit* artificial_livelock_accepting_state_added = ta->add_state(artificial_livelock_accepting_state);
-
-        // unique artificial_livelock_accepting_state
-        assert(artificial_livelock_accepting_state_added
-            == artificial_livelock_accepting_state);
-
         add_artificial_livelock_accepting_state(ta,
-            artificial_livelock_accepting_state_added);
+            artificial_livelock_accepting_state);
 
       }
 
@@ -160,6 +154,13 @@ namespace spot
       state_ta_explicit* artificial_livelock_accepting_state)
   {
 
+    state_ta_explicit* artificial_livelock_accepting_state_added =
+        testing_automata->add_state(artificial_livelock_accepting_state);
+
+    // unique artificial_livelock_accepting_state
+    assert(artificial_livelock_accepting_state_added
+        == artificial_livelock_accepting_state);
+
     ta::states_set_t states_set = testing_automata->get_states_set();
     ta::states_set_t::iterator it;
 
@@ -181,7 +182,7 @@ namespace spot
             {
               state_ta_explicit* dest = (*it_trans)->dest;
 
-              if (dest->is_livelock_accepting_state())
+              if (dest->is_livelock_accepting_state() && !dest->is_accepting_state())
                 {
                   conditions_to_livelock_accepting_states->insert(
                       (*it_trans)->condition);