diff --git a/socketio/__init__.py b/socketio/__init__.py
index f050d44..bfd68f6 100644
--- a/socketio/__init__.py
+++ b/socketio/__init__.py
@@ -11,7 +11,6 @@ from .namespace import Namespace, ClientNamespace
 from .middleware import WSGIApp, Middleware
 from .tornado import get_tornado_handler
 if sys.version_info >= (3, 5):  # pragma: no cover
-    # from .asyncio_client import AsyncClient
     from .asyncio_client import AsyncClient
     from .asyncio_server import AsyncServer
     from .asyncio_manager import AsyncManager
@@ -19,6 +18,7 @@ if sys.version_info >= (3, 5):  # pragma: no cover
     from .asyncio_redis_manager import AsyncRedisManager
     from .asgi import ASGIApp
 else:  # pragma: no cover
+    AsyncClient = None
     AsyncServer = None
     AsyncManager = None
     AsyncNamespace = None
diff --git a/socketio/asyncio_client.py b/socketio/asyncio_client.py
index b48515f..d1d8172 100644
--- a/socketio/asyncio_client.py
+++ b/socketio/asyncio_client.py
@@ -13,9 +13,9 @@ default_logger = logging.getLogger('socketio.client')
 
 
 class AsyncClient(client.Client):
-    """An Socket.IO client for asyncio.
+    """A Socket.IO client for asyncio.
 
-    This class implements a fully compliant Engine.IO web client with support
+    This class implements a fully compliant Socket.IO web client with support
     for websocket and long-polling transports.
 
     :param reconnection: ``True`` if the client should automatically attempt to
@@ -110,6 +110,7 @@ class AsyncClient(client.Client):
         """
         while True:
             await self.eio.wait()
+            await self.sleep(1)  # give the reconnect task time to start up
             if not self._reconnect_task:
                 break
             await self._reconnect_task
diff --git a/socketio/client.py b/socketio/client.py
index a33f86d..31bfe96 100644
--- a/socketio/client.py
+++ b/socketio/client.py
@@ -13,9 +13,9 @@ default_logger = logging.getLogger('socketio.client')
 
 
 class Client(object):
-    """An Socket.IO client.
+    """A Socket.IO client.
 
-    This class implements a fully compliant Engine.IO web client with support
+    This class implements a fully compliant Socket.IO web client with support
     for websocket and long-polling transports.
 
     :param reconnection: ``True`` if the client should automatically attempt to
@@ -214,6 +214,7 @@ class Client(object):
         """
         while True:
             self.eio.wait()
+            self.sleep(1)  # give the reconnect task time to start up
             if not self._reconnect_task:
                 break
             self._reconnect_task.join()