diff --git a/requirements.txt b/requirements.txt
index 05531f9d..0c583f0d 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,11 +1,11 @@
 aiohttp
 cassandra-driver >= 3.19.0, != 3.21.0
 click
 deprecated
 flask
 iso8601
 mypy_extensions
 psycopg2
 redis
-tenacity
+tenacity >= 6.2
 typing-extensions
diff --git a/swh/storage/proxies/retry.py b/swh/storage/proxies/retry.py
index d74f196e..6beaafa1 100644
--- a/swh/storage/proxies/retry.py
+++ b/swh/storage/proxies/retry.py
@@ -1,87 +1,83 @@
-# Copyright (C) 2019-2020 The Software Heritage developers
+# Copyright (C) 2019-2021 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
 
 import logging
 import traceback
 
 from tenacity import retry, stop_after_attempt, wait_random_exponential
 
 from swh.storage import get_storage
 from swh.storage.exc import StorageArgumentException
 from swh.storage.interface import StorageInterface
 
 logger = logging.getLogger(__name__)
 
 
 def should_retry_adding(retry_state) -> bool:
     """Retry if the error/exception is (probably) not about a caller error
 
     """
-    try:
-        attempt = retry_state.outcome
-    except AttributeError:
-        # tenacity < 5.0
-        attempt = retry_state
+    attempt = retry_state.outcome
 
     if attempt.failed:
         error = attempt.exception()
         if isinstance(error, StorageArgumentException):
             # Exception is due to an invalid argument
             return False
         elif isinstance(error, KeyboardInterrupt):
             return False
         else:
             # Other exception
             module = getattr(error, "__module__", None)
             if module:
                 error_name = error.__module__ + "." + error.__class__.__name__
             else:
                 error_name = error.__class__.__name__
             logger.warning(
                 "Retrying RPC call",
                 exc_info=False,
                 extra={
                     "swh_type": "storage_retry",
                     "swh_exception_type": error_name,
                     "swh_exception": traceback.format_exc(),
                 },
             )
             return True
     else:
         # No exception
         return False
 
 
 swh_retry = retry(
     retry=should_retry_adding,
     wait=wait_random_exponential(multiplier=1, max=10),
     stop=stop_after_attempt(3),
 )
 
 
 def retry_function(storage, attribute_name):
     @swh_retry
     def newf(*args, **kwargs):
         return getattr(storage, attribute_name)(*args, **kwargs)
 
     return newf
 
 
 class RetryingProxyStorage:
     """Storage implementation which retries adding objects when it specifically
        fails (hash collision, integrity error).
 
     """
 
     def __init__(self, storage):
         self.storage: StorageInterface = get_storage(**storage)
         for attribute_name in dir(StorageInterface):
             if attribute_name.startswith("_"):
                 continue
             attribute = getattr(self.storage, attribute_name)
             if hasattr(attribute, "__call__"):
                 setattr(
                     self, attribute_name, retry_function(self.storage, attribute_name)
                 )