diff --git a/hypothesis-python/setup.py b/hypothesis-python/setup.py
index 4fc0d3fe84..14c24b9efb 100644
--- a/hypothesis-python/setup.py
+++ b/hypothesis-python/setup.py
@@ -60,7 +60,7 @@ def local_file(name):
     "pytest": ["pytest>=4.6"],
     "dpcontracts": ["dpcontracts>=0.4"],
     "redis": ["redis>=3.0.0"],
-    "crosshair": ["hypothesis-crosshair>=0.0.14", "crosshair-tool>=0.0.73"],
+    "crosshair": ["hypothesis-crosshair>=0.0.16", "crosshair-tool>=0.0.74"],
     # zoneinfo is an odd one: every dependency is platform-conditional.
     "zoneinfo": [
         "tzdata>=2024.2 ; sys_platform == 'win32' or sys_platform == 'emscripten'",
diff --git a/hypothesis-python/tests/cover/test_health_checks.py b/hypothesis-python/tests/cover/test_health_checks.py
index 4133b6d1e7..3d0f04e536 100644
--- a/hypothesis-python/tests/cover/test_health_checks.py
+++ b/hypothesis-python/tests/cover/test_health_checks.py
@@ -64,6 +64,7 @@ def test(x):
     test()
 
 
+@pytest.mark.skipif(settings._current_profile == "crosshair", reason="nondeterministic")
 def test_suppressing_filtering_health_check():
     forbidden = set()