diff --git a/qutebrowser/browser/downloads.py b/qutebrowser/browser/downloads.py
index 6d12761f6..ab055cbf4 100644
--- a/qutebrowser/browser/downloads.py
+++ b/qutebrowser/browser/downloads.py
@@ -1038,7 +1038,7 @@ class DownloadManager(QAbstractListModel):
         """Override flags so items aren't selectable.
 
         The default would be Qt.ItemIsEnabled | Qt.ItemIsSelectable."""
-        return Qt.ItemIsEnabled
+        return Qt.ItemIsEnabled | Qt.ItemNeverHasChildren
 
     def rowCount(self, parent=QModelIndex()):
         """Get count of active downloads."""
diff --git a/qutebrowser/completion/models/base.py b/qutebrowser/completion/models/base.py
index f4b0cf4eb..b56444013 100644
--- a/qutebrowser/completion/models/base.py
+++ b/qutebrowser/completion/models/base.py
@@ -109,7 +109,8 @@ class BaseCompletionModel(QStandardItemModel):
         qtutils.ensure_valid(index)
         if index.parent().isValid():
             # item
-            return Qt.ItemIsEnabled | Qt.ItemIsSelectable
+            return (Qt.ItemIsEnabled | Qt.ItemIsSelectable |
+                    Qt.ItemNeverHasChildren)
         else:
             # category
             return Qt.NoItemFlags