diff --git a/spot/twaalgos/sbacc.cc b/spot/twaalgos/sbacc.cc
index c2db036ca..c64ca321f 100644
--- a/spot/twaalgos/sbacc.cc
+++ b/spot/twaalgos/sbacc.cc
@@ -64,6 +64,10 @@ namespace spot
           {
             common_in[d] &= e.acc;
             common_out[e.src] &= e.acc;
+            // Any state with an accepting edge labeled by true is a
+            // "true state".  We will merge all true states, and
+            // ignore other outgoing edges.  See issue #276 for an
+            // example.
             if (e.src == e.dst && e.cond == bddtrue
                 && old->acc().accepting(e.acc))
               {
@@ -89,6 +93,9 @@ namespace spot
     std::map<pair_t, unsigned> s2n;
 
     std::vector<std::pair<pair_t, unsigned>> todo;
+    auto* origin = new std::vector<unsigned>;
+    origin->reserve(ns);
+    res->set_named_prop("original-states", origin);
 
     auto new_state =
       [&](unsigned state, acc_cond::mark_t m) -> unsigned
@@ -107,6 +114,8 @@ namespace spot
         if (p.second)                // This is a new state
           {
             unsigned s = res->new_state();
+            assert(origin->size() == s);
+            origin->push_back(state);
             p.first->second = s;
             if (ts)
               {
@@ -175,6 +184,12 @@ namespace spot
       }
     res->merge_edges();
 
+    // Compose original-states with the any previously existing one.
+    if (auto old_orig_states =
+        old->get_named_prop<std::vector<unsigned>>("original-states"))
+      for (auto& s: *origin)
+        s = (*old_orig_states)[s];
+
     // If the automaton was marked as not complete or not universal,
     // and we have ignored some unreachable state, then it is possible
     // that the result becomes complete or universal.
diff --git a/spot/twaalgos/sbacc.hh b/spot/twaalgos/sbacc.hh
index 68067239d..11bc99e35 100644
--- a/spot/twaalgos/sbacc.hh
+++ b/spot/twaalgos/sbacc.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2015 Laboratoire de Recherche et Développement
+// Copyright (C) 2015, 2021 Laboratoire de Recherche et Développement
 // de l'Epita.
 //
 // This file is part of Spot, a model checking library.
@@ -23,8 +23,31 @@
 
 namespace spot
 {
+  /// \ingroup twa_algorithms
   /// \brief Transform an automaton to use state-based acceptance
   ///
-  /// This is independent on the acceptance condition used.
+  /// This transformation is independent on the acceptance condition
+  /// used.  The implementation supports alternating automata.
+  ///
+  /// It works by creating an automaton whose states correspond to
+  /// pairs (s,colors) for each edge entering state s with colors.  In
+  /// other words, we are pushing colors from the edges to their
+  /// outgoing states.  The implementation is also able to pull colors
+  /// on incoming states in cases where that helps.
+  ///
+  /// When called on automata that are already known to have
+  /// state-based acceptance, this function returns the input
+  /// unmodified, not a copy.
+  ///
+  /// Trues states (any state with an accepting self-loop labeled by
+  /// true) are merged in the process.
+  ///
+  /// The output will have a named property called "original-states"
+  /// that is a vector indexed by the produced states, and giving the
+  /// corresponding state in the input automaton.  If the input
+  /// automaton also had an "original-states" property, the two
+  /// vectors will be composed, so the `original-states[s]` in the
+  /// output will contains the value of `original-states[y] if state s
+  /// was created from state y.
   SPOT_API twa_graph_ptr sbacc(twa_graph_ptr aut);
 }
diff --git a/tests/python/sbacc.py b/tests/python/sbacc.py
index b0c457846..445845dbc 100644
--- a/tests/python/sbacc.py
+++ b/tests/python/sbacc.py
@@ -1,6 +1,6 @@
 # -*- mode: python; coding: utf-8 -*-
-# Copyright (C) 2017, 2018 Laboratoire de Recherche et Développement de l'Epita
-# (LRDE).
+# Copyright (C) 2017-2018, 2021 Laboratoire de Recherche et
+# Développement de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
 #
@@ -45,6 +45,7 @@ State: 2
 --END--""")
 
 s = spot.sbacc(aut)
+s.copy_state_names_from(aut)
 h = s.to_str('hoa')
 
 assert h == """HOA: v1
@@ -54,9 +55,9 @@ AP: 2 "a" "b"
 Acceptance: 2 Inf(0) | Inf(1)
 properties: trans-labels explicit-labels state-acc deterministic
 --BODY--
-State: 0
+State: 0 "0"
 [0] 1
-State: 1 {1}
+State: 1 "2" {1}
 [t] 1
 --END--"""
 
@@ -79,6 +80,7 @@ State: 2
 --END--""")
 
 d = spot.degeneralize(aut)
+d.copy_state_names_from(aut)
 h = d.to_str('hoa')
 
 assert h == """HOA: v1
@@ -89,8 +91,8 @@ acc-name: Buchi
 Acceptance: 1 Inf(0)
 properties: trans-labels explicit-labels state-acc deterministic
 --BODY--
-State: 0
+State: 0 "0#0"
 [0] 1
-State: 1 {0}
+State: 1 "2#0" {0}
 [t] 1
 --END--"""