diff --git a/src/tgbaalgos/cleanacc.cc b/src/tgbaalgos/cleanacc.cc
index cdfd776ba..5ee8027fc 100644
--- a/src/tgbaalgos/cleanacc.cc
+++ b/src/tgbaalgos/cleanacc.cc
@@ -47,6 +47,10 @@ namespace spot
 
     // Remove useless marks from the acceptance condition
     aut->set_acceptance(useful.count(), c.strip(useless, true));
+
+    // This may in turn cause even more set to be unused, because of
+    // some simplifications, so do it again.
+    return cleanup_acceptance(aut);
   }
 
 }
diff --git a/src/tgbatest/hoaparse.test b/src/tgbatest/hoaparse.test
index 7d9e663d1..a8953036a 100755
--- a/src/tgbatest/hoaparse.test
+++ b/src/tgbatest/hoaparse.test
@@ -1371,6 +1371,23 @@ State: 0
 [0&!1&!2] 0 {0}
 [!0&!1&!2] 0
 --END--
+HOA: v1
+States: 2
+Start: 0
+AP: 2 "a" "b"
+Acceptance: 4 (Fin(0) & Inf(1)) | (Fin(2) & Inf(3))
+properties: trans-labels explicit-labels state-acc deterministic
+--BODY--
+State: 0 {2}
+[0&!1] 1
+[!0&1] 0
+[0&1] 1
+State: 1 {1 2}
+[!0&!1] 1
+[0&!1] 1
+[!0&1] 1
+[0&1] 1
+--END--
 EOF
 
 expectok input -v --is-empty <<EOF
@@ -1407,6 +1424,23 @@ State: 0
 [0&!1&!2] 0 {0 5}
 [!0&!1&!2] 0 {5}
 --END--
+HOA: v1
+States: 2
+Start: 0
+AP: 2 "a" "b"
+Acceptance: 4 (Fin(0) & Inf(1)) | (Fin(2) & Inf(3))
+properties: trans-labels explicit-labels state-acc deterministic
+--BODY--
+State: 0 {2}
+[0&!1] 1
+[!0&1] 0
+[0&1] 1
+State: 1 {1 2}
+[!0&!1] 1
+[0&!1] 1
+[!0&1] 1
+[0&1] 1
+--END--
 EOF
 
 
@@ -1456,6 +1490,24 @@ State: 0
 [0&!1&!2] 0 {0 3}
 [!0&!1&!2] 0 {3}
 --END--
+HOA: v1
+States: 2
+Start: 0
+AP: 2 "a" "b"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels state-acc deterministic
+--BODY--
+State: 0
+[0&!1] 1
+[!0&1] 0
+[0&1] 1
+State: 1 {0}
+[!0&!1] 1
+[0&!1] 1
+[!0&1] 1
+[0&1] 1
+--END--
 EOF