diff --git a/synapse/types/__init__.py b/synapse/types/__init__.py
index d127be98ed..8b005ef84d 100644
--- a/synapse/types/__init__.py
+++ b/synapse/types/__init__.py
@@ -686,7 +686,7 @@ class AbstractMultiWriterStreamToken(metaclass=abc.ABCMeta):
     def bound_stream_token(self, max_stream: int) -> "Self":
         """Bound the stream positions to a maximum value"""
         # Shortcut if we're already under the bound
-        if max_stream <= self.get_max_stream_pos():
+        if self.get_max_stream_pos() <= max_stream:
             return self
 
         min_pos = min(self.stream, max_stream)