diff --git a/tests/core/test_schedule.py b/tests/core/test_schedule.py
index bfd6d9af180e5ec546eee588e03163f2e0845091..2afedc28bfaad07b8e818fadf08c3ef5a9c6de52 100644
--- a/tests/core/test_schedule.py
+++ b/tests/core/test_schedule.py
@@ -716,7 +716,7 @@ class TestComposition(unittest.TestCase):
 
         module1.outputs["Out"] >> Scale(1.0) >> module2.inputs["In"]
 
-        composition.connect(datetime(2000, 1, 1))
+        composition.connect()
         self.assertEqual(updates, ["A", "B"])
 
         composition.run(t_max=datetime(2000, 1, 2))
@@ -734,6 +734,72 @@ class TestComposition(unittest.TestCase):
             ],
         )
 
+    def test_dependencies_schedule_no_push_double(self):
+        start = datetime(2000, 1, 1)
+        info = fm.Info(time=start, grid=fm.NoGrid())
+
+        updates = []
+
+        def lambda_generator_1(t):
+            updates.append("A1")
+            return t.day
+
+        def lambda_generator_2(t):
+            if (t.day - 1) % 5 != 0:
+                return None
+            updates.append("A2")
+            return t.day
+
+        def lambda_component(inp, t):
+            updates.append("B")
+            return {"Out": inp["In1"]}
+
+        module1 = CallbackGenerator(
+            callbacks={
+                "Out1": (lambda_generator_1, info),
+                "Out2": (lambda_generator_2, info),
+            },
+            start=start,
+            step=timedelta(days=1),
+        )
+        module2 = CallbackComponent(
+            inputs={
+                "In1": fm.Info(time=None, grid=fm.NoGrid()),
+                "In2": fm.Info(time=None, grid=fm.NoGrid()),
+            },
+            outputs={
+                "Out": fm.Info(time=None, grid=fm.NoGrid()),
+            },
+            callback=lambda_component,
+            start=start,
+            step=timedelta(days=1),
+        )
+        composition = Composition([module1, module2])
+        composition.initialize()
+
+        module1.outputs["Out1"] >> Scale(1.0) >> module2.inputs["In1"]
+        module1.outputs["Out2"] >> Scale(1.0) >> module2.inputs["In2"]
+
+        composition.connect()
+        self.assertEqual(updates, ["A1", "A2", "B"])
+
+        composition.run(t_max=datetime(2000, 1, 2))
+        self.assertEqual(
+            updates,
+            [
+                "A1",
+                "A2",
+                "B",  # Connect
+                "A1",
+                "A1",
+                "A1",
+                "A1",
+                "A1",
+                "A2",
+                "B",  # Update B to 5
+            ],
+        )
+
     def test_dependency_fail(self):
         start = datetime(2000, 1, 1)
         info = fm.Info(time=start, grid=fm.NoGrid())