diff --git a/NEWS b/NEWS
index 4afbea16f..2c0734431 100644
--- a/NEWS
+++ b/NEWS
@@ -9,6 +9,10 @@ New in spot 2.9.5.dev (not yet released)
     performing an (unnecessary) second iteration even when the first
     one failed to reduce the automaton.  (Issue #442)
 
+  - When passed an incomplete automaton as input, tgba_determinize()
+    would sometimes produce a complete automaton but incorrectly mark
+    it as incomplete.
+
 New in spot 2.9.5 (2020-11-19)
 
   Bugs fixed:
diff --git a/spot/twaalgos/determinize.cc b/spot/twaalgos/determinize.cc
index 4aeddc497..fe4ed080c 100644
--- a/spot/twaalgos/determinize.cc
+++ b/spot/twaalgos/determinize.cc
@@ -926,9 +926,12 @@ namespace spot
                    { false, // state based
                        false, // inherently_weak
                        false, false, // deterministic
-                       true, // complete
+                       false, // complete
                        true // stutter inv
                        });
+    // completeness can only be improved.
+    if (aut->prop_complete().is_true())
+      res->prop_complete(true);
 
     // Given a safra_state get its associated state in output automata.
     // Required to create new edges from 2 safra-state