diff --git a/src/tests/satmin2.test b/src/tests/satmin2.test
index ba4bfb900..b459fa179 100755
--- a/src/tests/satmin2.test
+++ b/src/tests/satmin2.test
@@ -149,3 +149,30 @@ State: 0
 EOF
 
 diff output expected
+
+cat >foo.hoa <<EOF
+HOA: v1
+States: 1
+Start: 0
+Acceptance: 4 (Fin(0)&Inf(1)) | (Fin(2)&Inf(3))
+AP: 2 "b" "a"
+--BODY--
+State: 0
+ 0 {3}          /*{}*/
+ 0 {1 3}        /*{b}*/
+ 0 {2}          /*{a}*/
+ 0 {2 1}        /*{b, a}*/
+--END--
+EOF
+
+$autfilt --sat-minimize='acc="Inf(0)|Fin(1)",max-states=2' foo.hoa \
+	 --stats=%s >out
+test "`cat out`" = 1
+
+$autfilt --sat-minimize='acc="Inf(0)&Fin(1)",max-states=4' foo.hoa \
+	 --stats=%s >out && exit 1
+test -z "`cat out`"
+
+$autfilt --sat-minimize='acc="Inf(0)&Fin(1)|Inf(2)",states=1' foo.hoa \
+	 --stats=%s >out
+test "`cat out`" = 1
diff --git a/src/twaalgos/dtbasat.cc b/src/twaalgos/dtbasat.cc
index 3f15ded67..5b7743289 100644
--- a/src/twaalgos/dtbasat.cc
+++ b/src/twaalgos/dtbasat.cc
@@ -806,9 +806,11 @@ namespace spot
   }
 
   twa_graph_ptr
-  dtba_sat_minimize(const const_twa_graph_ptr& a, bool state_based)
+  dtba_sat_minimize(const const_twa_graph_ptr& a,
+		    bool state_based, int max_states)
   {
-    int n_states = stats_reachable(a).states;
+    int n_states = (max_states < 0) ?
+      stats_reachable(a).states : max_states + 1;
 
     twa_graph_ptr prev = nullptr;
     for (;;)
@@ -826,9 +828,10 @@ namespace spot
 
   twa_graph_ptr
   dtba_sat_minimize_dichotomy(const const_twa_graph_ptr& a,
-			      bool state_based)
+			      bool state_based, int max_states)
   {
-    int max_states = stats_reachable(a).states - 1;
+    if (max_states < 0)
+      max_states = stats_reachable(a).states - 1;
     int min_states = 1;
 
     twa_graph_ptr prev = nullptr;
diff --git a/src/twaalgos/dtbasat.hh b/src/twaalgos/dtbasat.hh
index 7553d8258..f5712f00e 100644
--- a/src/twaalgos/dtbasat.hh
+++ b/src/twaalgos/dtbasat.hh
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2013, 2014 Laboratoire de Recherche et Développement
-// de l'Epita.
+// Copyright (C) 2013, 2014, 2015 Laboratoire de Recherche et
+// Développement de l'Epita.
 //
 // This file is part of Spot, a model checking library.
 //
@@ -52,7 +52,8 @@ namespace spot
   /// If no smaller TBA exist, this returns a null pointer.
   SPOT_API twa_graph_ptr
   dtba_sat_minimize(const const_twa_graph_ptr& a,
-		    bool state_based = false);
+		    bool state_based = false,
+		    int max_states = -1);
 
   /// \brief Attempt to minimize a deterministic TBA with a SAT solver.
   ///
@@ -62,5 +63,6 @@ namespace spot
   /// If no smaller TBA exist, this returns a null pointer.
   SPOT_API twa_graph_ptr
   dtba_sat_minimize_dichotomy(const const_twa_graph_ptr& a,
-			      bool state_based = false);
+			      bool state_based = false,
+			      int max_states = -1);
 }
diff --git a/src/twaalgos/dtgbasat.cc b/src/twaalgos/dtgbasat.cc
index df2a5dfb0..da8ac354c 100644
--- a/src/twaalgos/dtgbasat.cc
+++ b/src/twaalgos/dtgbasat.cc
@@ -1156,9 +1156,11 @@ namespace spot
   dtgba_sat_minimize(const const_twa_graph_ptr& a,
 		     unsigned target_acc_number,
 		     const acc_cond::acc_code& target_acc,
-		     bool state_based)
+		     bool state_based,
+		     int max_states)
   {
-    int n_states = stats_reachable(a).states;
+    int n_states = (max_states < 0) ?
+      stats_reachable(a).states : max_states + 1;
 
     twa_graph_ptr prev = nullptr;
     for (;;)
@@ -1179,9 +1181,11 @@ namespace spot
   dtgba_sat_minimize_dichotomy(const const_twa_graph_ptr& a,
 			       unsigned target_acc_number,
 			       const acc_cond::acc_code& target_acc,
-			       bool state_based)
+			       bool state_based,
+			       int max_states)
   {
-    int max_states = stats_reachable(a).states - 1;
+    if (max_states < 1)
+      max_states = stats_reachable(a).states - 1;
     int min_states = 1;
 
     twa_graph_ptr prev = nullptr;
@@ -1223,6 +1227,7 @@ namespace spot
     bool sb = om.get("state-based", 0);
     bool dicho = om.get("dichotomy", 0);
     int states = om.get("states", -1);
+    int max_states = om.get("max-states", -1);
     int nacc = om.get("gba", -1);
     auto accstr = om.get_str("acc");
 
@@ -1260,17 +1265,17 @@ namespace spot
 
     tgba_complete_here(a);
 
-    if (sb)
-      a = sbacc(a);
+    if (sb && states == -1 && max_states == -1)
+      max_states = sbacc(a)->num_states();
 
     if (states == -1)
       {
 	if (!target_is_buchi || !a->acc().is_buchi())
 	  a = (dicho ? dtgba_sat_minimize_dichotomy : dtgba_sat_minimize)
-	    (a, nacc, target_acc, sb);
+	    (a, nacc, target_acc, sb, max_states);
 	else
 	  a = (dicho ? dtba_sat_minimize_dichotomy : dtba_sat_minimize)
-	    (a, sb);
+	    (a, sb, max_states);
       }
     else
       {
diff --git a/src/twaalgos/dtgbasat.hh b/src/twaalgos/dtgbasat.hh
index 35a4ad68f..4d2bfc58c 100644
--- a/src/twaalgos/dtgbasat.hh
+++ b/src/twaalgos/dtgbasat.hh
@@ -62,7 +62,8 @@ namespace spot
   dtgba_sat_minimize(const const_twa_graph_ptr& a,
 		     unsigned target_acc_number,
 		     const acc_cond::acc_code& target_acc,
-		     bool state_based = false);
+		     bool state_based = false,
+		     int max_states = -1);
 
   /// \brief Attempt to minimize a deterministic TGBA with a SAT solver.
   ///
@@ -74,7 +75,8 @@ namespace spot
   dtgba_sat_minimize_dichotomy(const const_twa_graph_ptr& a,
 			       unsigned target_acc_number,
 			       const acc_cond::acc_code& target_acc,
-			       bool state_based = false);
+			       bool state_based = false,
+			       int max_states = -1);
 
   /// \brief High-level interface to SAT-based minimization
   ///