diff --git a/lib/galaxy/managers/hdas.py b/lib/galaxy/managers/hdas.py
index 17abe5063337..09354dd71ebc 100644
--- a/lib/galaxy/managers/hdas.py
+++ b/lib/galaxy/managers/hdas.py
@@ -21,6 +21,8 @@
     desc,
     false,
     func,
+    nulls_first,
+    nulls_last,
     select,
     true,
 )
@@ -347,8 +349,8 @@ def __init__(self, hda_manager: HDAManager, dataset_manager: datasets.DatasetMan
         self.sort_map = {
             StoredItemOrderBy.NAME_ASC: asc(model.HistoryDatasetAssociation.name),
             StoredItemOrderBy.NAME_DSC: desc(model.HistoryDatasetAssociation.name),
-            StoredItemOrderBy.SIZE_ASC: asc(model.Dataset.total_size),
-            StoredItemOrderBy.SIZE_DSC: desc(model.Dataset.total_size),
+            StoredItemOrderBy.SIZE_ASC: nulls_first(asc(model.Dataset.total_size)),
+            StoredItemOrderBy.SIZE_DSC: nulls_last(desc(model.Dataset.total_size)),
             StoredItemOrderBy.UPDATE_TIME_ASC: asc(model.HistoryDatasetAssociation.update_time),
             StoredItemOrderBy.UPDATE_TIME_DSC: desc(model.HistoryDatasetAssociation.update_time),
         }
diff --git a/test/integration/test_storage_cleaner.py b/test/integration/test_storage_cleaner.py
index c358536c3244..51485f0ede2e 100644
--- a/test/integration/test_storage_cleaner.py
+++ b/test/integration/test_storage_cleaner.py
@@ -6,7 +6,10 @@
 from uuid import uuid4
 
 from galaxy_test.base.decorators import requires_new_history
-from galaxy_test.base.populators import DatasetPopulator
+from galaxy_test.base.populators import (
+    DatasetPopulator,
+    skip_without_tool,
+)
 from galaxy_test.driver import integration_util
 
 
@@ -39,6 +42,43 @@ def test_discarded_datasets_monitoring_and_cleanup(self):
             "datasets", test_datasets, dataset_ids, delete_resource_uri=f"histories/{history_id}/contents"
         )
 
+    @requires_new_history
+    @skip_without_tool("cat_data_and_sleep")
+    def test_discarded_datasets_with_null_size_are_sorted_correctly(self):
+        history_id = self.dataset_populator.new_history(f"History for discarded datasets {uuid4()}")
+        test_datasets = [
+            StoredItemDataForTests(name=f"TestDataset01_{uuid4()}", size=10),
+            StoredItemDataForTests(name=f"TestDataset02_{uuid4()}", size=50),
+        ]
+        dataset_ids = self._create_datasets_in_history_with(history_id, test_datasets)
+
+        # Run a tool on the first dataset and delete the output before completing the job
+        # so it has a null size in the database
+        inputs = {
+            "input1": {"src": "hda", "id": dataset_ids[0]},
+            "sleep_time": 10,
+        }
+        run_response = self.dataset_populator.run_tool_raw(
+            "cat_data_and_sleep",
+            inputs,
+            history_id,
+        )
+        null_size_dataset = run_response.json()["outputs"][0]
+        self.dataset_populator.delete_dataset(history_id, null_size_dataset["id"], stop_job=True)
+        # delete the other datasets too
+        for dataset_id in dataset_ids:
+            self.dataset_populator.delete_dataset(history_id, dataset_id)
+
+        # Check the dataset size sorting is correct [0, 10, 50]
+        item_names_forward_order = [null_size_dataset["name"], test_datasets[0].name, test_datasets[1].name]
+        item_names_reverse_order = list(reversed(item_names_forward_order))
+        expected_order_by_map = {
+            "size-asc": item_names_forward_order,
+            "size-dsc": item_names_reverse_order,
+        }
+        for order_by, expected_ordered_names in expected_order_by_map.items():
+            self._assert_order_is_expected("storage/datasets/discarded", order_by, expected_ordered_names)
+
     @requires_new_history
     def test_archived_histories_monitoring_and_cleanup(self):
         test_histories = self._build_test_items(resource_name="History")