diff --git a/src/aioquic/quic/connection.py b/src/aioquic/quic/connection.py
index b99c4ab85..49c6e65d8 100644
--- a/src/aioquic/quic/connection.py
+++ b/src/aioquic/quic/connection.py
@@ -342,10 +342,14 @@ def __init__(
 
         if self._is_client:
             self._original_destination_connection_id = self._peer_cid.cid
+            self._next_uni_id = 2
+            self._next_bidi_id = 0
         else:
             self._original_destination_connection_id = (
                 original_destination_connection_id
             )
+            self._next_uni_id = 3
+            self._next_bidi_id = 1
 
         # logging
         self._logger = QuicConnectionAdapter(
@@ -623,10 +627,10 @@ 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
+        if is_unidirectional:
+            return self._next_uni_id
+        else:
+            return self._next_bidi_id
 
     def get_timer(self) -> Optional[float]:
         """
@@ -1291,12 +1295,17 @@ def _get_or_create_stream_for_send(self, stream_id: int) -> QuicStream:
                 streams_blocked = self._streams_blocked_bidi
 
             # create stream
+            is_unidirectional = stream_is_unidirectional(stream_id)
             stream = self._streams[stream_id] = QuicStream(
                 stream_id=stream_id,
                 max_stream_data_local=max_stream_data_local,
                 max_stream_data_remote=max_stream_data_remote,
-                readable=not stream_is_unidirectional(stream_id),
+                readable=not is_unidirectional
             )
+            if is_unidirectional:
+                self._next_uni_id = stream_id + 4
+            else:
+                self._next_bidi_id = stream_id + 4
 
             # mark stream as blocked if needed
             if stream_id // 4 >= max_streams: