diff --git a/src/tests/safra.cc b/src/tests/safra.cc
index 549513c0c..747cd5530 100644
--- a/src/tests/safra.cc
+++ b/src/tests/safra.cc
@@ -26,6 +26,7 @@
 #include "hoaparse/public.hh"
 #include "ltlparse/public.hh"
 #include "twaalgos/dotty.hh"
+#include "twaalgos/hoa.hh"
 
 
 int main(int argc, char* argv[])
@@ -57,5 +58,11 @@ int main(int argc, char* argv[])
     }
   res->merge_transitions();
 
-  spot::dotty_reachable(std::cout, res);
+  if (argc >= 4 && !strncmp(argv[3], "-H", 2))
+    {
+      spot::hoa_reachable(std::cout, res, "t");
+      std::cout << std::endl;
+    }
+  else
+    spot::dotty_reachable(std::cout, res);
 }
diff --git a/src/tests/safra.test b/src/tests/safra.test
index 2156270b6..5aeb2a2f7 100755
--- a/src/tests/safra.test
+++ b/src/tests/safra.test
@@ -41,28 +41,31 @@ State: 1
 EOF
 
 cat >out.exp << EOF
-digraph G {
-  rankdir=LR
-  node [shape="circle"]
-  I [label="", style=invis, width=0]
-  I -> 0
-  0 [label="0"]
-  0 -> 1 [label="a"]
-  1 [label="1"]
-  1 -> 2 [label="a\n{0}"]
-  1 -> 3 [label="!a & b\n{3}"]
-  2 [label="2"]
-  2 -> 1 [label="a"]
-  2 -> 3 [label="!a & b"]
-  3 [label="3"]
-  3 -> 0 [label="a & !b"]
-  3 -> 2 [label="a & b"]
-  3 -> 3 [label="!a & b"]
-}
+HOA: v1
+States: 4
+Start: 0
+AP: 2 "a" "b"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels trans-acc deterministic
+--BODY--
+State: 0
+[0] 1
+State: 1
+[0] 2 {0}
+[!0&1] 3
+State: 2
+[0] 1
+[!0&1] 3
+State: 3
+[0&!1] 0
+[0&1] 2
+[!0&1] 3
+--END--
 EOF
 
-run 0 ../safra --hoa double_a.hoa > out.dot
-diff out.dot out.exp
+run 0 ../safra --hoa double_a.hoa -H > out.hoa
+diff out.hoa out.exp
 
 cat >double_b.hoa << EOF
 HOA: v1
@@ -83,33 +86,36 @@ State: 1
 EOF
 
 cat >out.exp << EOF
-digraph G {
-  rankdir=LR
-  node [shape="circle"]
-  I [label="", style=invis, width=0]
-  I -> 0
-  0 [label="0"]
-  0 -> 1 [label="a"]
-  1 [label="1"]
-  1 -> 1 [label="a & !b"]
-  1 -> 2 [label="a & b"]
-  1 -> 3 [label="!a & b\n{0}"]
-  2 [label="2"]
-  2 -> 3 [label="!a & b\n{0}"]
-  2 -> 4 [label="a & !b"]
-  2 -> 5 [label="a & b"]
-  3 [label="3"]
-  3 -> 0 [label="a & !b"]
-  3 -> 2 [label="a & b"]
-  3 -> 3 [label="!a & b\n{0}"]
-  4 [label="4"]
-  4 -> 1 [label="a\n{0}"]
-  4 -> 3 [label="!a & b\n{0}"]
-  5 [label="5"]
-  5 -> 1 [label="a\n{0}"]
-  5 -> 3 [label="!a & b\n{0}"]
-}
+HOA: v1
+States: 6
+Start: 0
+AP: 2 "a" "b"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels trans-acc deterministic
+--BODY--
+State: 0
+[0] 1
+State: 1
+[0&!1] 1
+[0&1] 2
+[!0&1] 3 {0}
+State: 2
+[!0&1] 3 {0}
+[0&!1] 4
+[0&1] 5
+State: 3
+[0&!1] 0
+[0&1] 2
+[!0&1] 3 {0}
+State: 4
+[0] 1 {0}
+[!0&1] 3 {0}
+State: 5
+[0] 1 {0}
+[!0&1] 3 {0}
+--END--
 EOF
 
-run 0 ../safra --hoa double_b.hoa > out.dot
-diff out.dot out.exp
+run 0 ../safra --hoa double_b.hoa -H > out.hoa
+diff out.hoa out.exp
diff --git a/src/twaalgos/safra.cc b/src/twaalgos/safra.cc
index 7070d8980..f26484258 100644
--- a/src/twaalgos/safra.cc
+++ b/src/twaalgos/safra.cc
@@ -26,6 +26,19 @@
 
 namespace spot
 {
+  namespace
+  {
+    // Used to remove all acceptance whos value is above max_acc
+    void remove_dead_acc(twa_graph_ptr& aut, unsigned max_acc)
+    {
+      assert(max_acc < 32);
+      unsigned mask = (1 << max_acc) - 1;
+      for (auto& t: aut->transitions())
+        {
+          t.acc &= mask;
+        }
+    }
+  }
   auto
   safra_state::compute_succs(const const_twa_graph_ptr& aut,
                              const std::vector<unsigned>& bddnums,
@@ -293,10 +306,10 @@ namespace spot
     auto res = make_twa_graph(aut->get_dict());
     res->copy_ap_of(aut);
     res->prop_copy(aut,
-                   { true, // state based
+                   { false, // state based
                    true, // inherently_weak
-                   true, // deterministic
-                   false // stutter inv
+                   false, // deterministic
+                   true // stutter inv
                    });
 
     // Given a safra_state get its associated state in output automata.
@@ -309,6 +322,7 @@ namespace spot
     seen.insert(std::make_pair(init, num));
     std::deque<safra_state> todo;
     todo.push_back(init);
+    unsigned sets = 0;
     while (!todo.empty())
       {
         using succs_t = safra_state::succs_t;
@@ -332,12 +346,22 @@ namespace spot
                 seen.insert(std::make_pair(s.first, dst_num));
               }
             if (s.first.color_ != -1U)
-              res->new_transition(src_num, dst_num, num2bdd[s.second],
-                                  {s.first.color_});
+              {
+                res->new_transition(src_num, dst_num, num2bdd[s.second],
+                                    {s.first.color_});
+                // We only care about green acc
+                if (s.first.color_ % 2 == 0)
+                  sets = std::max(s.first.color_ + 1, sets);
+              }
             else
               res->new_transition(src_num, dst_num, num2bdd[s.second]);
           }
       }
+    //
+    remove_dead_acc(res, sets);
+    res->set_acceptance(sets, acc_cond::acc_code::parity(false, false, sets));
+    res->prop_deterministic(true);
+    res->prop_state_based_acc(false);
     return res;
   }
 }