diff --git a/spot/twaalgos/synthesis.cc b/spot/twaalgos/synthesis.cc
index 3bfeba5b7..c0a655d73 100644
--- a/spot/twaalgos/synthesis.cc
+++ b/spot/twaalgos/synthesis.cc
@@ -354,7 +354,7 @@ namespace spot
         dst_cond_color_t key{std::make_pair(dst, ocond.id()),
                              color};
         auto [it, inserted] =
-            player_map.try_emplace(key, aut->num_states() + 1);
+            player_map.try_emplace(key, aut->num_states());
         if (!inserted)
           return it->second;
         unsigned ns = aut->new_state();
diff --git a/tests/core/ltlsynt.test b/tests/core/ltlsynt.test
index d2427ea1a..4fbba5fd8 100644
--- a/tests/core/ltlsynt.test
+++ b/tests/core/ltlsynt.test
@@ -421,6 +421,12 @@ ltlsynt --outs=p1 -f "$f" -x"dpa-simul=1" --simpl=sat | grep 'States: 2'
 ltlsynt --outs=p1 -f "$f" -x"dpa-simul=1" --simpl=bisim-sat | grep 'States: 2'
 ltlsynt --outs=p1 -f "$f" -x"dpa-simul=1" --simpl=bwoa-sat | grep 'States: 4'
 
+# The following used to raise an exception because of a bug in
+# split_2step_fast_here().
+for i in 0 1 2 3 4 5; do
+    ltlsynt --ins=a -f 'GFa <-> GFb' --simplify=$i | grep 'States: 1'
+done
+
 cat >exp <<EOF
 REALIZABLE
 aag 34 4 3 2 27