diff --git a/src/plumpy/processes.py b/src/plumpy/processes.py
index 61070ec7..5a9ee115 100644
--- a/src/plumpy/processes.py
+++ b/src/plumpy/processes.py
@@ -1316,13 +1316,27 @@ def execute(self) -> dict[str, Any] | None:
         """
         from .reentry import _get_runner
 
-        if self.has_terminated():
-            return self.result()
+        if not self.has_terminated():
+            coro = self.step_until_terminated()
+            with _get_runner() as runner:
+                result = runner.run(coro)
+
+            return result
+
+        else:
+            self.result()
+
+    async def step_until_terminated(self) -> Any:
+        """If the process has not terminated,
+        run the current step and wait until the step finished.
 
-        runner = _get_runner()
-        with runner as runner:
-            return runner.run(self.step_until_terminated())
-        # return asyncio.run(self.step_until_terminated())
+        This is the function run by the event loop (not ``step``).
+
+        """
+        while not self.has_terminated():
+            await self.step()
+
+        return await self.future()
 
     @ensure_not_closed
     async def step(self) -> None:
@@ -1378,18 +1392,6 @@ async def step(self) -> None:
             self._stepping = False
             self._set_interrupt_action(None)
 
-    async def step_until_terminated(self) -> Any:
-        """If the process has not terminated,
-        run the current step and wait until the step finished.
-
-        This is the function run by the event loop (not ``step``).
-
-        """
-        while not self.has_terminated():
-            await self.step()
-
-        return await self.future()
-
     # endregion
 
     @ensure_not_closed
diff --git a/tests/test_processes.py b/tests/test_processes.py
index eefd581d..767442e4 100644
--- a/tests/test_processes.py
+++ b/tests/test_processes.py
@@ -41,7 +41,6 @@ def on_kill(self, msg):
             super().on_kill(msg)
 
 
-@pytest.mark.usefixtures('custom_event_loop_policy')
 def test_process_is_savable():
     proc = utils.DummyProcess()
     assert isinstance(proc, Savable)
@@ -71,7 +70,6 @@ async def task(self, steps: list):
 
 
 class TestProcess:
-    @pytest.mark.usefixtures('custom_event_loop_policy')
     def test_spec(self):
         """
         Check that the references to specs are doing the right thing...
@@ -586,7 +584,6 @@ def run(self):
         proc = StackTest()
         proc.execute()
 
-    @pytest.mark.usefixtures('custom_event_loop_policy')
     def test_process_stack_multiple(self):
         """
         Run multiple and nested processes to make sure the process stack is always correct
@@ -622,7 +619,6 @@ def run(self):
 
         assert len(expect_true) == n_run * 3
 
-    @pytest.mark.usefixtures('custom_event_loop_policy')
     def test_process_nested(self):
         """
         Run multiple and nested processes to make sure the process stack is always correct