diff --git a/spot/misc/bitvect.hh b/spot/misc/bitvect.hh
index 7c54658a5..d91653381 100644
--- a/spot/misc/bitvect.hh
+++ b/spot/misc/bitvect.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2013-2020 Laboratoire de Recherche et Développement
+// Copyright (C) 2013-2021 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -364,6 +364,45 @@ namespace spot
       return !(other < *this);
     }
 
+    template<typename F>
+    void foreach_set_index(F callback) const
+    {
+      const size_t bpb = 8 * sizeof(bitvect::block_t);
+      size_t rest = size() % bpb;
+      for (size_t i = 0; i <= block_count_ - 1; ++i)
+        {
+          block_t b = storage_[i];
+          if ((i == block_count_ - 1) && rest)
+            // The last block might not be fully used, scan only the
+            // relevant portion.
+            b &= (1UL << rest) - 1;
+          if (b != 0)
+            {
+              unsigned base = i * bpb;
+#if __GNUC__
+              // This version is probably faster on sparse bitsets.
+              do
+                {
+                  unsigned bit = __builtin_ctzl(b);
+                  b ^= 1UL << bit;
+                  callback(base + bit);
+                }
+              while (b);
+#else
+              unsigned bit = 0;
+              do
+                {
+                  if (b & 1)
+                    callback(base + bit);
+                  ++bit;
+                  b >>= 1;
+                }
+              while (b);
+#endif
+            }
+        }
+    }
+
     friend SPOT_API bitvect* make_bitvect(size_t bitcount);
 
     /// Print a bitvect.
diff --git a/tests/core/bitvect.cc b/tests/core/bitvect.cc
index d8b0750d5..cf74dcddf 100644
--- a/tests/core/bitvect.cc
+++ b/tests/core/bitvect.cc
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2013-2016, 2018 Laboratoire de Recherche et
+// Copyright (C) 2013-2016, 2018, 2021 Laboratoire de Recherche et
 // Développement de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -35,6 +35,11 @@ static void ruler()
   std::cout << "\n\n";
 }
 
+static void print_callback(unsigned t)
+{
+  std::cout << t << ',';
+}
+
 #define ECHO(name) std::cout << #name": " << *name << '\n'
 
 int main()
@@ -65,9 +70,24 @@ int main()
   *x |= *w;
   ECHO(x);
 
+  std::cout << "foreach in v: ";
+  v->foreach_set_index(print_callback);
+  std::cout << '\n';
+  std::cout << "foreach in w: ";
+  w->foreach_set_index(print_callback);
+  std::cout << '\n';
+  std::cout << "foreach in x: ";
+  x->foreach_set_index(print_callback);
+  std::cout << '\n';
+
   std::cout << "subset? " << w->is_subset_of(*x)
             << ' ' << v->is_subset_of(*w) << '\n';
 
+  *x -= *x;
+  std::cout << "foreach in x-x: ";
+  x->foreach_set_index(print_callback);
+  std::cout << '\n';
+
   delete v;
   delete w;
   delete x;
diff --git a/tests/core/bitvect.test b/tests/core/bitvect.test
index 6da55d655..c76b3808f 100755
--- a/tests/core/bitvect.test
+++ b/tests/core/bitvect.test
@@ -1,7 +1,7 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2013, 2015, 2016 Laboratoire de Recherche et Développement
-# de l'Epita (LRDE).
+# Copyright (C) 2013, 2015, 2016, 2021 Laboratoire de Recherche et
+# Développement de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
 #
@@ -23,7 +23,7 @@
 
 set -e
 
-run 0 ../bitvect | tee stderr
+run 0 ../bitvect | sed 's/ $//' | tee stderr
 cat >expected <<EOF
 
    0_________1_________2_________3_________4_________5_________6_________7_____
@@ -43,7 +43,11 @@ w: 000000000010110000000000000000100000000001
 
 x: 000000000000000000000000000000000000000000000000000000000000100000000010000
 x: 000000000010110000000000000000100000000001000000000000000000100000000010000
+foreach in v: 7,10,12,
+foreach in w: 10,12,13,30,41,
+foreach in x: 10,12,13,30,41,60,70,
 subset? 1 0
+foreach in x-x:
 
    0_________1_________2_________3_________4_________5_________6_________7_____
    0123456789012345678901234567890123456789012345678901234567890123456789012345