diff --git a/src/aioquic/quic/connection.py b/src/aioquic/quic/connection.py
index b99c4ab85..4fa965388 100644
--- a/src/aioquic/quic/connection.py
+++ b/src/aioquic/quic/connection.py
@@ -5,6 +5,7 @@
 from dataclasses import dataclass
 from enum import Enum
 from functools import partial
+from itertools import count
 from typing import Any, Deque, Dict, FrozenSet, List, Optional, Sequence, Set, Tuple
 
 from .. import tls
@@ -416,6 +417,13 @@ def __init__(
             0x31: (self._handle_datagram_frame, EPOCHS("01")),
         }
 
+        if self._is_client:
+            self._bidi_stream_id = count(0, 4)
+            self._uni_stream_id = count(2, 4)
+        else:
+            self._bidi_stream_id = count(1, 4)
+            self._uni_stream_id = count(3, 4)
+
     @property
     def configuration(self) -> QuicConfiguration:
         return self._configuration
@@ -623,10 +631,7 @@ def get_next_available_stream_id(self, is_unidirectional=False) -> int:
         """
         Return the stream ID for the next stream created by this endpoint.
         """
-        stream_id = (int(is_unidirectional) << 1) | int(not self._is_client)
-        while stream_id in self._streams or stream_id in self._streams_finished:
-            stream_id += 4
-        return stream_id
+        return next(self._uni_stream_id if is_unidirectional else self._bidi_stream_id)
 
     def get_timer(self) -> Optional[float]:
         """