diff --git a/sdk/cosmos/azure-cosmos/README.md b/sdk/cosmos/azure-cosmos/README.md
index 9930ae0530a5..7c29d7a73df7 100644
--- a/sdk/cosmos/azure-cosmos/README.md
+++ b/sdk/cosmos/azure-cosmos/README.md
@@ -468,7 +468,7 @@ For more information on TTL, see [Time to Live for Azure Cosmos DB data][cosmos_
 ### Using the asynchronous client (Preview)
 
 The asynchronous cosmos client is a separate client that looks and works in a similar fashion to the existing synchronous client. However, the async client needs to be imported separately and its methods need to be used with the async/await keywords.
-The Async client needs to be initialized and closed after usage. The example below shows how to do so by using the client's __aenter__() and close() methods.
+The Async client needs to be initialized and closed after usage, which can be done manually or with the use of a context manager. The example below shows how to do so manually.
 
 ```Python
 from azure.cosmos.aio import CosmosClient
@@ -481,7 +481,6 @@ CONTAINER_NAME = 'products'
 
 async def create_products():
     client = CosmosClient(URL, credential=KEY)
-    await client.__aenter__()
     database = client.get_database_client(DATABASE_NAME)
     container = database.get_container_client(CONTAINER_NAME)
     for i in range(10):
diff --git a/sdk/cosmos/azure-cosmos/azure/cosmos/_base.py b/sdk/cosmos/azure-cosmos/azure/cosmos/_base.py
index aacafbd41458..b99a569fc1e9 100644
--- a/sdk/cosmos/azure-cosmos/azure/cosmos/_base.py
+++ b/sdk/cosmos/azure-cosmos/azure/cosmos/_base.py
@@ -242,7 +242,7 @@ def GetHeaders(  # pylint: disable=too-many-statements,too-many-branches
         headers[http_constants.HttpHeaders.XDate] = datetime.datetime.utcnow().strftime("%a, %d %b %Y %H:%M:%S GMT")
 
     if cosmos_client_connection.master_key or cosmos_client_connection.resource_tokens:
-        authorization = auth.get_authorization_header(
+        authorization = auth._get_authorization_header(
             cosmos_client_connection, verb, path, resource_id, IsNameBased(resource_id), resource_type, headers
         )
         # urllib.quote throws when the input parameter is None
diff --git a/sdk/cosmos/azure-cosmos/azure/cosmos/auth.py b/sdk/cosmos/azure-cosmos/azure/cosmos/auth.py
index 7c239ccec7ac..cca10023ca5f 100644
--- a/sdk/cosmos/azure-cosmos/azure/cosmos/auth.py
+++ b/sdk/cosmos/azure-cosmos/azure/cosmos/auth.py
@@ -36,11 +36,11 @@ def GetAuthorizationHeader(
     warnings.warn("This method has been deprecated and will be removed from the SDK in a future release.",
                   DeprecationWarning)
 
-    return get_authorization_header(
+    return _get_authorization_header(
         cosmos_client_connection, verb, path, resource_id_or_fullname, is_name_based, resource_type, headers)
 
 
-def get_authorization_header(
+def _get_authorization_header(
         cosmos_client_connection, verb, path, resource_id_or_fullname, is_name_based, resource_type, headers
 ):
     """Gets the authorization header.
diff --git a/sdk/cosmos/azure-cosmos/samples/examples_async.py b/sdk/cosmos/azure-cosmos/samples/examples_async.py
index 97edcd7c9519..88a714fef0c4 100644
--- a/sdk/cosmos/azure-cosmos/samples/examples_async.py
+++ b/sdk/cosmos/azure-cosmos/samples/examples_async.py
@@ -19,16 +19,7 @@ async def examples_async():
     # which can only be used within async methods like examples_async() here
 
     # Since this is an asynchronous client, in order to properly use it you also have to warm it up and close it down.
-    # One way to do it would be like below (all of these statements would be necessary if you want to do it this way).
-
-    async_client = CosmosClient(url, key)
-    await async_client.__aenter__()
-
-    # [CODE LOGIC HERE, CLOSING WITH THE STATEMENT BELOW WHEN DONE]
-
-    await async_client.close()
-
-    # Or better, you can use the `async with` keywords like below to start your clients - these keywords
+    # We recommend using the `async with` keywords like below to start your clients - these keywords
     # create a context manager that automatically warms up, initializes, and cleans up the client, so you don't have to.
 
     # [START create_client]