diff --git a/src/scwidgets/exercise/_widget_code_exercise.py b/src/scwidgets/exercise/_widget_code_exercise.py
index eba08a3..f211080 100644
--- a/src/scwidgets/exercise/_widget_code_exercise.py
+++ b/src/scwidgets/exercise/_widget_code_exercise.py
@@ -176,8 +176,13 @@ def __init__(
                     "code and params do no match:  " + compatibility_result
                 )
 
-        CheckableWidget.__init__(self, check_registry, exercise_key)
-        ExerciseWidget.__init__(self, exercise_registry, exercise_key)
+        name = kwargs.get("name", exercise_key)
+        CheckableWidget.__init__(self, check_registry, name)
+        if exercise_registry is not None:
+            ExerciseWidget.__init__(self, exercise_registry, exercise_key)
+        else:
+            # otherwise ExerciseWidget constructor will raise an error
+            ExerciseWidget.__init__(self, None, None)
 
         self._code = code
         self._output = CueOutput()
diff --git a/tests/test_code.py b/tests/test_code.py
index 5c399c9..529262b 100644
--- a/tests/test_code.py
+++ b/tests/test_code.py
@@ -355,3 +355,21 @@ def test_figure(self):
         assert isinstance(code_ex.figure, Figure)
         assert code_ex.output.figure is code_ex.figure
         assert code_ex.outputs[0] is code_ex.output
+
+    def test_consrtuction_with_registries(self):
+        """Because the exercise key is used for the `ExerciseRegistry` and the
+        `CheckRegistry` we need to ensure the `CodeExercise` can be run with
+        each individual one and both"""
+        CodeExercise(
+            exercise_key="some_key",
+            check_registry=CheckRegistry(),
+        )
+        CodeExercise(
+            exercise_key="some_key",
+            exercise_registry=ExerciseRegistry(),
+        )
+        CodeExercise(
+            exercise_key="some_key",
+            check_registry=CheckRegistry(),
+            exercise_registry=ExerciseRegistry(),
+        )