diff --git a/trio/_highlevel_open_tcp_listeners.py b/trio/_highlevel_open_tcp_listeners.py
index e3c0f3d91f..33cb7e1a64 100644
--- a/trio/_highlevel_open_tcp_listeners.py
+++ b/trio/_highlevel_open_tcp_listeners.py
@@ -3,13 +3,13 @@
 import errno
 import math
 import sys
-import warnings
 from collections.abc import Awaitable, Callable
 
 import trio
 from trio import TaskStatus
 
 from . import socket as tsocket
+from ._deprecate import warn_deprecated
 
 if sys.version_info < (3, 11):
     from exceptiongroup import ExceptionGroup
@@ -48,9 +48,11 @@ def _compute_backlog(backlog: int | None) -> int:
     # https://github.com/golang/go/issues/5030
     if backlog == math.inf:
         backlog = None
-        warnings.warn(
-            "Accepting infinity for backlog for compatibility, please use `None` instead.",
-            stacklevel=2,
+        warn_deprecated(
+            thing="math.inf as a backlog",
+            version="0.23.0",
+            instead="None",
+            issue=2842,
         )
     if not isinstance(backlog, int) and backlog is not None:
         raise TypeError(f"backlog must be an int or None, not {backlog!r}")
diff --git a/trio/_tests/test_highlevel_open_tcp_listeners.py b/trio/_tests/test_highlevel_open_tcp_listeners.py
index e1fe845f0a..23d6f794e0 100644
--- a/trio/_tests/test_highlevel_open_tcp_listeners.py
+++ b/trio/_tests/test_highlevel_open_tcp_listeners.py
@@ -10,7 +10,13 @@
 import pytest
 
 import trio
-from trio import SocketListener, open_tcp_listeners, open_tcp_stream, serve_tcp
+from trio import (
+    SocketListener,
+    TrioDeprecationWarning,
+    open_tcp_listeners,
+    open_tcp_stream,
+    serve_tcp,
+)
 from trio.abc import HostnameResolver, SendStream, SocketFactory
 from trio.testing import open_stream_to_socket_listener
 
@@ -378,6 +384,17 @@ async def test_open_tcp_listeners_backlog() -> None:
             assert listener.socket.backlog == expected  # type: ignore[attr-defined]
 
 
+async def test_open_tcp_listeners_backlog_inf_warning() -> None:
+    fsf = FakeSocketFactory(99)
+    tsocket.set_custom_socket_factory(fsf)
+    with pytest.warns(TrioDeprecationWarning):
+        listeners = await open_tcp_listeners(0, backlog=float("inf"))  # type: ignore[arg-type]
+    assert listeners
+    for listener in listeners:
+        # `backlog` only exists on FakeSocket
+        assert listener.socket.backlog == 0xFFFF  # type: ignore[attr-defined]
+
+
 async def test_open_tcp_listeners_backlog_float_error() -> None:
     fsf = FakeSocketFactory(99)
     tsocket.set_custom_socket_factory(fsf)