diff --git a/NEWS b/NEWS
index a193ea39d..03283857b 100644
--- a/NEWS
+++ b/NEWS
@@ -173,6 +173,10 @@ New in spot 2.9.5.dev (not yet released)
   - tgba_determinize() could create parity automata using more colors
     than necessary.
 
+  - 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 436b8303a..c3a981353 100644
--- a/spot/twaalgos/determinize.cc
+++ b/spot/twaalgos/determinize.cc
@@ -933,9 +933,12 @@ 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
diff --git a/tests/python/298.py b/tests/python/298.py
index 51f9f35a1..d4865c440 100644
--- a/tests/python/298.py
+++ b/tests/python/298.py
@@ -25,9 +25,16 @@ a1 = spot.automaton("""genltl --dac=51 | ltl2tgba --med |""")
 a1 = spot.degeneralize_tba(a1)
 r1 = spot.tgba_determinize(a1, True, False, False)
 assert r1.num_sets() == 3
+assert a1.prop_complete().is_false();
+# This used to fail in 2.9.5 and earlier.
+assert r1.prop_complete().is_maybe();
+assert spot.is_complete(r1)
 
 a2 = spot.automaton("""genltl --dac=51 | ltl2tgba --high |""")
 a2 = spot.degeneralize_tba(a2)
 r2 = spot.tgba_determinize(a2, True, False, False)
 # This used to fail in 2.9.5 and earlier.
 assert r2.num_sets() == 3
+assert a2.prop_complete().is_false();
+assert r2.prop_complete().is_maybe();
+assert spot.is_complete(r2)