diff --git a/NEWS b/NEWS
index d025625a3..fed67a1ca 100644
--- a/NEWS
+++ b/NEWS
@@ -32,6 +32,9 @@ New in spot 2.9.0.dev (not yet released)
     spot::translator class when creating deterministic automata with
     generic acceptance.
 
+  - remove_fin() learned a trick to remove some superfluous
+    transitions.
+
   Bugs fixed:
 
   - Work around undefined behavior reported by clang 10.0.0's UBsan.
diff --git a/spot/twaalgos/remfin.cc b/spot/twaalgos/remfin.cc
index d34110e62..38774f60b 100644
--- a/spot/twaalgos/remfin.cc
+++ b/spot/twaalgos/remfin.cc
@@ -667,6 +667,20 @@ namespace spot
           trace << "main_sets " << main_sets << "\nmain_add "
                 << main_add << '\n';
 
+          // If the SCC is rejecting, there is no need for clone.
+          // Pretend we don't interesect any Fin.
+          if (si.is_rejecting_scc(n))
+            intersects_fin = false;
+
+          // Edges that are already satisfying the acceptance of the
+          // main copy do not need to be duplicated in the clones, so
+          // we fill allacc_edge to remember those.  Of course this is
+          // only needed if the main copy can be accepting and if we
+          // will create clones.
+          std::vector<bool> allacc_edge(aut->edge_vector().size(), false);
+          auto main_acc = res->acc().restrict_to(main_sets | main_add);
+          bool check_main_acc = intersects_fin && !main_acc.is_f();
+
           // Create the main copy
           for (auto s: states)
             for (auto& t: aut->out(s))
@@ -675,11 +689,14 @@ namespace spot
                 if (sbacc || SPOT_LIKELY(si.scc_of(t.dst) == n))
                   a = (t.acc & main_sets) | main_add;
                 res->new_edge(s, t.dst, t.cond, a);
+                // remember edges that are completely accepting
+                if (check_main_acc && main_acc.accepting(a))
+                  allacc_edge[aut->edge_number(t)] = true;
               }
 
           // We do not need any other copy if the SCC is non-accepting,
           // of if it does not intersect any Fin.
-          if (!intersects_fin || si.is_rejecting_scc(n))
+          if (!intersects_fin)
             continue;
 
           // Create clones
@@ -698,7 +715,12 @@ namespace spot
                     auto ns = state_map[s];
                     for (auto& t: aut->out(s))
                       {
-                        if ((t.acc & r) || si.scc_of(t.dst) != n)
+                        if ((t.acc & r) || si.scc_of(t.dst) != n
+                            // edges that are already accepting in the
+                            // main copy need not be copied in the
+                            // clone, since cycles going through them
+                            // are already accepted.
+                            || allacc_edge[aut->edge_number(t)])
                           continue;
                         auto nd = state_map[t.dst];
                         res->new_edge(ns, nd, t.cond, (t.acc & k) | a);
diff --git a/tests/core/ltl2dstar4.test b/tests/core/ltl2dstar4.test
index a0db47ec4..dfa004805 100755
--- a/tests/core/ltl2dstar4.test
+++ b/tests/core/ltl2dstar4.test
@@ -1,6 +1,6 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2013, 2014, 2015, 2017 Laboratoire de Recherche et
+# Copyright (C) 2013-2015, 2017, 2020 Laboratoire de Recherche et
 # Développement de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
@@ -34,7 +34,7 @@ ltlfilt -f '(GFa -> GFb) & (GFc -> GFd)' -l |
 ltl2dstar --ltl2nba=spin:ltl2tgba@-s $STR - - |
 autfilt --tgba --stats '%S %E %A %s %e %t %a %d' |
 tee out
-test "`cat out`" = '9 144 4 25 149 416 2 0'
+test "`cat out`" = '9 144 4 18 98 202 2 0'
 
 ltlfilt -f '(GFa -> GFb) & (GFc -> GFd)' -l |
 ltl2dstar --ltl2nba=spin:ltl2tgba@-s $STR - - |
diff --git a/tests/python/remfin.py b/tests/python/remfin.py
index b6f53d453..7eb9ab4d2 100644
--- a/tests/python/remfin.py
+++ b/tests/python/remfin.py
@@ -1,6 +1,6 @@
 # -*- mode: python; coding: utf-8 -*-
-# Copyright (C) 2015-2018  Laboratoire de Recherche et Développement
-# de l'Epita
+# Copyright (C) 2015-2018, 2020 Laboratoire de Recherche et Développement de
+# l'Epita
 #
 # This file is part of Spot, a model checking library.
 #
@@ -67,3 +67,29 @@ assert(a.prop_universal().is_maybe())
 assert(a.prop_unambiguous().is_maybe())
 assert(a.is_deterministic() == True)
 assert(a.is_unambiguous() == True)
+
+a = spot.automaton("""
+HOA: v1
+States: 3
+Start: 0
+AP: 2 "a" "b"
+acc-name: Buchi
+Acceptance: 5 Inf(0)&Fin(4) | Inf(2)&Inf(3) | Inf(1)
+--BODY--
+State: 0 {3}
+[t] 0
+[0] 1 {1}
+[!0] 2 {0 4}
+State: 1 {3}
+[1] 0
+[0&1] 1 {0}
+[!0&1] 2 {2 4}
+State: 2
+[!1] 0
+[0&!1] 1 {0}
+[!0&!1] 2 {0 4}
+--END--
+""")
+b = spot.remove_fin(a)
+size = (b.num_states(), b.num_edges())
+assert size == (5, 17);