diff --git a/python/sites/mach.txt b/python/sites/mach.txt
index 55cc6fb..51bf67d 100644
--- a/python/sites/mach.txt
+++ b/python/sites/mach.txt
@@ -141,5 +141,5 @@ pypi-optional:glean-sdk==52.7.0:telemetry will not be collected
 # Mach gracefully handles the case where `psutil` is unavailable.
 # We aren't (yet) able to pin packages in automation, so we have to
 # support down to the oldest locally-installed version (5.4.2).
-pypi-optional:psutil>=5.4.2,<=5.9.4:telemetry will be missing some data
-pypi-optional:zstandard>=0.11.1,<=0.22.0:zstd archives will not be possible to extract
+pypi-optional:psutil>=5.4.2,<=5.10.0:telemetry will be missing some data
+pypi-optional:zstandard>=0.11.1,<=0.24.0:zstd archives will not be possible to extract