diff --git a/.github/workflows/tests.yaml b/.github/workflows/tests.yaml
index c852936b..a7ad601a 100644
--- a/.github/workflows/tests.yaml
+++ b/.github/workflows/tests.yaml
@@ -21,6 +21,7 @@ jobs:
       fail-fast: false
       matrix:
         include:
+          - {python: '3.13'}
           - {python: '3.12'}
           - {name: Windows, python: '3.12', os: windows-latest}
           - {name: Mac, python: '3.12', os: macos-latest}
diff --git a/tests/test_leak.py b/tests/test_leak.py
index 260f4844..b786e072 100644
--- a/tests/test_leak.py
+++ b/tests/test_leak.py
@@ -1,31 +1,25 @@
 from __future__ import annotations
 
 import gc
-import platform
 
-import pytest
-
-from markupsafe import _escape_inner  # type: ignore[attr-defined]
 from markupsafe import escape
 
 
-@pytest.mark.skipif(
-    _escape_inner.__module__ == "markupsafe._native",
-    reason="only test memory leak with speedups",
-)
 def test_markup_leaks() -> None:
     counts = set()
+    # Try to start with a "clean" count. Works for PyPy but not 3.13 JIT.
+    gc.collect()
 
-    for _i in range(20):
-        for _j in range(1000):
+    for _ in range(20):
+        for _ in range(1000):
             escape("foo")
             escape("<foo>")
             escape("foo")
             escape("<foo>")
 
-        if platform.python_implementation() == "PyPy":
-            gc.collect()
-
         counts.add(len(gc.get_objects()))
 
-    assert len(counts) == 1
+    # Some implementations, such as PyPy and Python 3.13 JIT, end up with 2
+    # counts rather than one. Presumably this is internals stabilizing. A leak
+    # would presumably have a different count every loop.
+    assert len(counts) < 3
diff --git a/tox.ini b/tox.ini
index 8fb07c26..e961b1a3 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,6 +1,6 @@
 [tox]
 envlist =
-    py3{12,11,10,9,8}
+    py3{13,12,11,10,9,8}
     pypy310
     style
     typing