diff --git a/NEWS b/NEWS
index 3d6803e13..e16cb623c 100644
--- a/NEWS
+++ b/NEWS
@@ -12,6 +12,10 @@ New in spot 2.5.3.dev  (not yet released)
   - autfilt learned --is-colored to filter automata that use
     exactly one acceptance set per mark or transition.
 
+  - autfilt learned --has-univ-branching and --has-exist-branching
+    to keep automata that have universal branching, or that make
+    non-deterministic choices.
+
   - ltlcross, ltldo, and autcross learned shorthands to call
     delag, ltl2dra, ltl2dgra, and nba2dpa.
 
diff --git a/bin/autfilt.cc b/bin/autfilt.cc
index 20306d037..018086289 100644
--- a/bin/autfilt.cc
+++ b/bin/autfilt.cc
@@ -104,6 +104,8 @@ enum {
   OPT_EXCLUSIVE_AP,
   OPT_GENERALIZED_RABIN,
   OPT_GENERALIZED_STREETT,
+  OPT_HAS_EXIST_BRANCHING,
+  OPT_HAS_UNIV_BRANCHING,
   OPT_HIGHLIGHT_NONDET,
   OPT_HIGHLIGHT_NONDET_EDGES,
   OPT_HIGHLIGHT_NONDET_STATES,
@@ -187,6 +189,11 @@ static const argp_option options[] =
     { "unique", 'u', nullptr, 0,
       "do not output the same automaton twice (same in the sense that they "
       "are isomorphic)", 0 },
+    { "has-exist-branching", OPT_HAS_EXIST_BRANCHING, nullptr, 0,
+      "keep automata that use existential branching (i.e., make "
+      "non-deterministic choices)", 0 },
+    { "has-univ-branching", OPT_HAS_UNIV_BRANCHING, nullptr, 0,
+      "keep alternating automata that use universal branching", 0 },
     { "is-colored", OPT_IS_COLORED, nullptr, 0,
       "keep colored automata (i.e., exactly one acceptance mark per "
       "transition or state)", 0 },
@@ -560,6 +567,8 @@ static struct opt_t
 }* opt;
 
 static bool opt_merge = false;
+static bool opt_has_univ_branching = false;
+static bool opt_has_exist_branching = false;
 static bool opt_is_alternating = false;
 static bool opt_is_colored = false;
 static bool opt_is_complete = false;
@@ -829,6 +838,12 @@ parse_opt(int key, char* arg, struct argp_state*)
         opt_gsa = GSA_UNIQUE_FIN;
       opt_gra = GRA_NO;
       break;
+    case OPT_HAS_EXIST_BRANCHING:
+      opt_has_exist_branching = true;
+      break;
+    case OPT_HAS_UNIV_BRANCHING:
+      opt_has_univ_branching = true;
+      break;
     case OPT_HIGHLIGHT_NONDET:
       {
         int v = arg ? to_pos_int(arg, "--highlight-nondet") : 1;
@@ -1363,6 +1378,10 @@ namespace
         }
       if (opt_nondet_states_set)
         matched &= opt_nondet_states.contains(spot::count_nondet_states(aut));
+      if (opt_has_univ_branching)
+        matched &= !aut->is_existential();
+      if (opt_has_exist_branching)
+        matched &= !is_universal(aut);
       if (opt_is_deterministic)
         {
           matched &= is_deterministic(aut);
diff --git a/tests/core/alternating.test b/tests/core/alternating.test
index 6a1798f0f..270ccd650 100755
--- a/tests/core/alternating.test
+++ b/tests/core/alternating.test
@@ -53,7 +53,7 @@ State: 6 "t"
 --END--
 EOF
 
-autfilt --dot=bans alt.hoa >alt.dot
+autfilt --has-univ-branch --has-exist-branch --dot=bans alt.hoa >alt.dot
 
 cat >expect.dot <<EOF
 digraph "" {
@@ -267,6 +267,8 @@ State: 2
 --END--
 EOF
 
+autfilt --has-exist-branch ex3 && exit 1
+
 autfilt -q --equivalent-to=ex1 ex2
 autfilt -q --included-in=ex1 ex2
 autfilt -q --equivalent-to=ex1 ex3 && exit 1
@@ -654,7 +656,7 @@ State: 4 "t"
 --END--
 EOF
 
-run 0 autfilt --dot='sbarf(Lato)' ex8 > ex8.dot
+run 0 autfilt --has-exist-branch --dot='sbarf(Lato)' ex8 > ex8.dot
 
 cat >expect8.dot<<EOF
 digraph "SLAA for c R (c | G(a & b) | (F!b & F!a))" {
@@ -734,7 +736,7 @@ State: 2
 --END--
 EOF
 
-run 0 autfilt --dot='baryf(Lato)' ex9 > ex9.dot
+run 0 autfilt -v --has-exist-branch --dot='baryf(Lato)' ex9 > ex9.dot
 
 cat >expect9.dot <<EOF
 digraph "" {