diff --git a/asyncpg/connect_utils.py b/asyncpg/connect_utils.py
index 6957fa79..4cc87fc8 100644
--- a/asyncpg/connect_utils.py
+++ b/asyncpg/connect_utils.py
@@ -4,6 +4,7 @@
 # This module is part of asyncpg and is released under
 # the Apache 2.0 License: http://www.apache.org/licenses/LICENSE-2.0
 
+from __future__ import annotations
 
 import asyncio
 import collections
@@ -59,7 +60,7 @@ class _ConnectionParameters(typing.NamedTuple):
     sslmode: SSLMode
     ssl_negotiation: SSLNegotiation
     server_settings: typing.Optional[typing.Dict[str, str]]
-    target_session_attrs: "SessionAttribute"
+    target_session_attrs: SessionAttribute
     krbsrvname: typing.Optional[str]
     gsslib: str
 
@@ -129,7 +130,7 @@ def _read_password_file(passfile: pathlib.Path) \
 def _read_password_from_pgpass(
     *,
     passfile: pathlib.Path,
-    hosts: "Sequence[str]",
+    hosts: Sequence[str],
     ports: typing.List[int],
     database: str,
     user: str
@@ -166,7 +167,7 @@ def _read_password_from_pgpass(
 
 
 def _validate_port_spec(
-    hosts: "Sequence[object]", port: typing.Union[int, typing.List[int]]
+    hosts: Sequence[object], port: typing.Union[int, typing.List[int]]
 ) -> typing.List[int]:
     if isinstance(port, list):
         # If there is a list of ports, its length must