diff --git a/cylc/flow/task_outputs.py b/cylc/flow/task_outputs.py
index 6c0bd8f8ea2..644b7b0dd3c 100644
--- a/cylc/flow/task_outputs.py
+++ b/cylc/flow/task_outputs.py
@@ -299,3 +299,18 @@ def msg_sort_key(item):
         except ValueError:
             ind = 999
         return (ind, item[_MESSAGE] or '')
+
+    @staticmethod
+    def output_sort_key(item):
+        """Compare by output order.
+
+        Examples:
+
+            >>> this = TaskOutputs.output_sort_key
+            >>> sorted(['finished', 'started',  'custom'], key=this)
+            ['started', 'custom', 'finished']
+        """
+        if item in TASK_OUTPUTS:
+            return TASK_OUTPUTS.index(item)
+        # Sort custom outputs after started.
+        return TASK_OUTPUTS.index(TASK_OUTPUT_STARTED) + .5
diff --git a/cylc/flow/task_pool.py b/cylc/flow/task_pool.py
index dbe60fb7292..d9c418e7137 100644
--- a/cylc/flow/task_pool.py
+++ b/cylc/flow/task_pool.py
@@ -1820,6 +1820,7 @@ def _set_outputs_itask(
                 itask.point, itask.tdef, outputs)
 
         changed = False
+        outputs = sorted(outputs, key=itask.state.outputs.output_sort_key)
         for output in outputs:
             if itask.state.outputs.is_completed(output):
                 LOG.info(f"output {itask.identity}:{output} completed already")
diff --git a/tests/integration/test_task_pool.py b/tests/integration/test_task_pool.py
index be1f335d45b..e076e6a4495 100644
--- a/tests/integration/test_task_pool.py
+++ b/tests/integration/test_task_pool.py
@@ -1499,6 +1499,38 @@ async def test_set_outputs_live(
         )
 
 
+async def test_set_outputs_live2(
+    flow,
+    scheduler,
+    start,
+    log_filter,
+):
+    """Assert that optional outputs are satisfied before completion
+    outputs to prevent incomplete task warnings.
+    """
+    id_ = flow(
+        {
+            'scheduler': {'allow implicit tasks': 'True'},
+            'scheduling': {'graph': {
+                'R1': """
+                    foo:a => apple
+                    foo:b => boat
+                """}},
+            'runtime': {'foo': {'outputs': {
+                'a': 'xylophone',
+                'b': 'yacht'}}}
+        }
+    )
+    schd = scheduler(id_)
+
+    async with start(schd) as log:
+        schd.pool.set_prereqs_and_outputs(["1/foo"], None, None, ['all'])
+        assert not log_filter(
+            log,
+            contains="did not complete required outputs: ['a', 'b']"
+        )
+
+
 async def test_set_outputs_future(
     flow,
     scheduler,