diff --git a/src/ert/scheduler/job.py b/src/ert/scheduler/job.py
index c90bae21bd6..37e97a3fb82 100644
--- a/src/ert/scheduler/job.py
+++ b/src/ert/scheduler/job.py
@@ -145,7 +145,7 @@ async def __call__(
                 )
                 logger.warning(message)
                 self.returncode = asyncio.Future()
-                self.started = asyncio.Event()
+                self.started.clear()
             else:
                 await self._send(State.FAILED)
 
diff --git a/src/ert/scheduler/scheduler.py b/src/ert/scheduler/scheduler.py
index 201837cadda..26c60749c85 100644
--- a/src/ert/scheduler/scheduler.py
+++ b/src/ert/scheduler/scheduler.py
@@ -26,7 +26,11 @@
 from websockets.client import connect
 
 from ert.constant_filenames import CERT_FILE
-from ert.job_queue.queue import EVTYPE_ENSEMBLE_CANCELLED, EVTYPE_ENSEMBLE_STOPPED
+from ert.job_queue.queue import (
+    CLOSE_PUBLISHER_SENTINEL,
+    EVTYPE_ENSEMBLE_CANCELLED,
+    EVTYPE_ENSEMBLE_STOPPED,
+)
 from ert.scheduler.driver import SIGNAL_OFFSET, Driver
 from ert.scheduler.event import FinishedEvent
 from ert.scheduler.job import Job
@@ -106,6 +110,7 @@ def __init__(
         self._ens_id = ens_id
         self._ee_cert = ee_cert
         self._ee_token = ee_token
+        self._publisher_done = asyncio.Event()
 
     def kill_all_jobs(self) -> None:
         assert self._loop
@@ -187,7 +192,11 @@ async def _publisher(self) -> None:
         ):
             while True:
                 event = await self._events.get()
+                if event == CLOSE_PUBLISHER_SENTINEL:
+                    self._publisher_done.set()
+                    return
                 await conn.send(event)
+                self._events.task_done()
 
     def add_dispatch_information_to_jobs_file(self) -> None:
         for job in self._jobs.values():
@@ -225,6 +234,9 @@ async def _monitor_and_handle_tasks(
                         raise task_exception
 
             if not self.is_active():
+                if self._ee_uri is not None:
+                    await self._events.put(CLOSE_PUBLISHER_SENTINEL)
+                    await self._publisher_done.wait()
                 for task in self._job_tasks.values():
                     if task.cancelled():
                         continue
diff --git a/tests/integration_tests/analysis/test_es_update.py b/tests/integration_tests/analysis/test_es_update.py
index 79452284a5c..39f4648cb27 100644
--- a/tests/integration_tests/analysis/test_es_update.py
+++ b/tests/integration_tests/analysis/test_es_update.py
@@ -164,7 +164,6 @@ def sample_prior(nx, ny):
         )
 
 
-@pytest.mark.skip(reason="Very flaky with scheduler")
 @pytest.mark.integration_test
 @pytest.mark.usefixtures("copy_snake_oil_field", "using_scheduler")
 def test_update_multiple_param():
diff --git a/tests/integration_tests/scheduler/test_openpbs_driver.py b/tests/integration_tests/scheduler/test_openpbs_driver.py
index 669b049c741..a4740a3ab0f 100644
--- a/tests/integration_tests/scheduler/test_openpbs_driver.py
+++ b/tests/integration_tests/scheduler/test_openpbs_driver.py
@@ -41,7 +41,6 @@ def queue_name_config():
 def test_that_openpbs_driver_ignores_qstat_flakiness(
     text_to_ignore, caplog, capsys, create_mock_flaky_qstat
 ):
-
     create_mock_flaky_qstat(text_to_ignore)
     with open("poly.ert", mode="a+", encoding="utf-8") as f:
         f.write("QUEUE_SYSTEM TORQUE\nNUM_REALIZATIONS 1")
diff --git a/tests/unit_tests/scheduler/test_job.py b/tests/unit_tests/scheduler/test_job.py
index 32ede9be8f4..2cc8d4b3fcd 100644
--- a/tests/unit_tests/scheduler/test_job.py
+++ b/tests/unit_tests/scheduler/test_job.py
@@ -67,8 +67,9 @@ async def test_submitted_job_is_cancelled(realization, mock_event):
 
     await asyncio.wait_for(job.started._mock_waited, 5)
 
-    assert job_task.cancel()
+    job_task.cancel()
     await job_task
+
     await assert_scheduler_events(
         scheduler, [State.SUBMITTING, State.PENDING, State.ABORTING, State.ABORTED]
     )
diff --git a/tests/unit_tests/scheduler/test_scheduler.py b/tests/unit_tests/scheduler/test_scheduler.py
index 33e2b8974e7..bf2463570ca 100644
--- a/tests/unit_tests/scheduler/test_scheduler.py
+++ b/tests/unit_tests/scheduler/test_scheduler.py
@@ -8,6 +8,7 @@
 from typing import List
 
 import pytest
+import websockets
 from cloudevents.http import from_json
 
 from ert.config import QueueConfig
@@ -476,6 +477,47 @@ async def mock_failure(message, *args, **kwargs):
     raise RuntimeError(message)
 
 
+async def _mock_ws(set_when_done: asyncio.Event, handler, port: int):
+    async with websockets.server.serve(handler, "127.0.0.1", port):
+        await set_when_done.wait()
+
+
+async def test_scheduler_publishes_to_websocket(
+    mock_driver, realization, unused_tcp_port
+):
+    set_when_done = asyncio.Event()
+
+    events_received: List[str] = []
+
+    async def mock_ws_event_handler(websocket):
+        nonlocal events_received
+        async for message in websocket:
+            events_received.append(message)
+        await websocket.close()
+
+    websocket_server_task = asyncio.create_task(
+        _mock_ws(set_when_done, mock_ws_event_handler, unused_tcp_port)
+    )
+
+    driver = mock_driver()
+    sch = scheduler.Scheduler(
+        driver, [realization], ee_uri=f"ws://127.0.0.1:{unused_tcp_port}"
+    )
+    await sch.execute()
+    # publisher_done is set only if CLOSE_PUBLISHER_SENTINEL was received
+    assert sch._publisher_done.is_set()
+
+    set_when_done.set()
+    await websocket_server_task
+    assert [
+        json.loads(event)["data"]["queue_event_type"] for event in events_received
+    ] == ["SUBMITTED", "PENDING", "RUNNING", "SUCCESS"]
+
+    assert (
+        sch._events.empty()
+    ), "Schedulers internal event queue must be empty before finish"
+
+
 @pytest.mark.timeout(5)
 async def test_that_driver_poll_exceptions_are_propagated(mock_driver, realization):
     driver = mock_driver()