diff --git a/swh/core/api/__init__.py b/swh/core/api/__init__.py
--- a/swh/core/api/__init__.py
+++ b/swh/core/api/__init__.py
@@ -1,4 +1,4 @@
-# Copyright (C) 2015-2020  The Software Heritage developers
+# Copyright (C) 2015-2022  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
@@ -7,7 +7,6 @@
 import functools
 import inspect
 import logging
-import pickle
 from typing import (
     Any,
     Callable,
@@ -325,36 +324,18 @@
 
         exception = None
 
-        # TODO: only old servers send pickled error; stop trying to unpickle
-        # after they are all upgraded
-        try:
-            if status_class == 4:
-                data = self._decode_response(response, check_status=False)
-                if isinstance(data, dict):
-                    # TODO: remove "exception" key check once all servers
-                    # are using new schema
-                    exc_data = data["exception"] if "exception" in data else data
-                    for exc_type in self.reraise_exceptions:
-                        if exc_type.__name__ == exc_data["type"]:
-                            exception = exc_type(*exc_data["args"])
-                            break
-                    else:
-                        exception = RemoteException(payload=exc_data, response=response)
-                else:
-                    exception = pickle.loads(data)
-
-            elif status_class == 5:
-                data = self._decode_response(response, check_status=False)
-                if "exception_pickled" in data:
-                    exception = pickle.loads(data["exception_pickled"])
-                else:
-                    # TODO: remove "exception" key check once all servers
-                    # are using new schema
-                    exc_data = data["exception"] if "exception" in data else data
-                    exception = RemoteException(payload=exc_data, response=response)
-
-        except (TypeError, pickle.UnpicklingError):
-            raise RemoteException(payload=data, response=response)
+        if status_class == 4:
+            exc_data = self._decode_response(response, check_status=False)
+            for exc_type in self.reraise_exceptions:
+                if exc_type.__name__ == exc_data["type"]:
+                    exception = exc_type(*exc_data["args"])
+                    break
+            else:
+                exception = RemoteException(payload=exc_data, response=response)
+
+        elif status_class == 5:
+            exc_data = self._decode_response(response, check_status=False)
+            exception = RemoteException(payload=exc_data, response=response)
 
         if exception:
             raise exception from None
diff --git a/swh/core/api/tests/test_rpc_client.py b/swh/core/api/tests/test_rpc_client.py
--- a/swh/core/api/tests/test_rpc_client.py
+++ b/swh/core/api/tests/test_rpc_client.py
@@ -1,4 +1,4 @@
-# Copyright (C) 2018-2019  The Software Heritage developers
+# Copyright (C) 2018-2022  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
@@ -110,13 +110,11 @@
     assert str(exc_info.value.args[0]) == error_message
 
 
-def _exception_response(exception, status_code, old_exception_schema=False):
+def _exception_response(exception, status_code):
     def callback(request, context):
         assert request.headers["Content-Type"] == "application/x-msgpack"
         context.headers["Content-Type"] = "application/x-msgpack"
         exc_dict = exception_to_dict(exception)
-        if old_exception_schema:
-            exc_dict = {"exception": exc_dict}
         context.content = msgpack_dumps(exc_dict)
         context.status_code = status_code
         return context.content
@@ -124,8 +122,7 @@
     return callback
 
 
-@pytest.mark.parametrize("old_exception_schema", [False, True])
-def test_client_reraise_exception(rpc_client, requests_mock, old_exception_schema):
+def test_client_reraise_exception(rpc_client, requests_mock):
     """
     Exception caught server-side and whitelisted will be raised again client-side.
     """
@@ -137,7 +134,6 @@
         content=_exception_response(
             exception=ReraiseException(error_message),
             status_code=400,
-            old_exception_schema=old_exception_schema,
         ),
     )
 
@@ -147,18 +143,8 @@
     assert str(exc_info.value) == error_message
 
 
-@pytest.mark.parametrize(
-    "status_code, old_exception_schema",
-    [
-        (400, False),
-        (500, False),
-        (400, True),
-        (500, True),
-    ],
-)
-def test_client_raise_remote_exception(
-    rpc_client, requests_mock, status_code, old_exception_schema
-):
+@pytest.mark.parametrize("status_code", [400, 500])
+def test_client_raise_remote_exception(rpc_client, requests_mock, status_code):
     """
     Exception caught server-side and not whitelisted will be wrapped and raised
     as a RemoteException client-side.
@@ -171,7 +157,6 @@
         content=_exception_response(
             exception=Exception(error_message),
             status_code=status_code,
-            old_exception_schema=old_exception_schema,
         ),
     )