diff --git a/agentex/src/domain/repositories/task_message_repository.py b/agentex/src/domain/repositories/task_message_repository.py
index 8d5e1e30..92ab9ac2 100644
--- a/agentex/src/domain/repositories/task_message_repository.py
+++ b/agentex/src/domain/repositories/task_message_repository.py
@@ -19,15 +19,13 @@ class TaskMessageRepository(MongoDBCRUDRepository[TaskMessageEntity]):
     # These will be created once at startup, not per request
     INDEXES = [
         {
-            "keys": [("task_id", pymongo.ASCENDING), ("created_at", pymongo.ASCENDING)],
+            "keys": [
+                ("task_id", pymongo.ASCENDING),
+                ("created_at", pymongo.DESCENDING),
+            ],
             "name": "task_id_created_at_idx",
             "description": "Compound index for querying messages by task_id and sorting by created_at",
         },
-        {
-            "keys": [("task_id", pymongo.ASCENDING)],
-            "name": "task_id_idx",
-            "description": "Single index for task_id queries and delete operations",
-        },
         {
             "keys": [
                 ("task_id", pymongo.ASCENDING),
@@ -40,7 +38,7 @@ class TaskMessageRepository(MongoDBCRUDRepository[TaskMessageEntity]):
             "keys": [
                 ("task_id", pymongo.ASCENDING),
                 ("content.type", pymongo.ASCENDING),
-                ("created_at", pymongo.ASCENDING),
+                ("created_at", pymongo.DESCENDING),
             ],
             "name": "task_id_content_type_created_at_idx",
             "description": "Compound index for filtering messages by task_id, content type, and sorting by created_at",
diff --git a/agentex/src/domain/repositories/task_state_repository.py b/agentex/src/domain/repositories/task_state_repository.py
index 16e43147..d2dab1ae 100644
--- a/agentex/src/domain/repositories/task_state_repository.py
+++ b/agentex/src/domain/repositories/task_state_repository.py
@@ -21,12 +21,8 @@ class TaskStateRepository(MongoDBCRUDRepository[StateEntity]):
         {
             "keys": [("task_id", pymongo.ASCENDING), ("agent_id", pymongo.ASCENDING)],
             "name": "task_agent_compound_idx",
-            "description": "Compound index for get_by_task_and_agent queries",
-        },
-        {
-            "keys": [("task_id", pymongo.ASCENDING)],
-            "name": "task_id_idx",
-            "description": "Single index for task_id queries",
+            "unique": True,
+            "description": "Unique compound index for get_by_task_and_agent queries",
         },
         {
             "keys": [("agent_id", pymongo.ASCENDING)],