diff --git a/tools/run_tests/build_artifact_python.sh b/tools/run_tests/build_artifact_python.sh
index f2c10aba7b1..5768485ca2a 100755
--- a/tools/run_tests/build_artifact_python.sh
+++ b/tools/run_tests/build_artifact_python.sh
@@ -39,18 +39,20 @@ then
   pip install -rrequirements.txt
 fi
 
+# The bdist_wheel_grpc_custom command is finicky about command output ordering
+# and thus ought to be run in a shell command separate of others. Further, it
+# trashes the actual bdist_wheel output, so it should be run first so that
+# bdist_wheel may be run unmolested.
 GRPC_PYTHON_USE_CUSTOM_BDIST=0  \
 GRPC_PYTHON_BUILD_WITH_CYTHON=1 \
 ${SETARCH_CMD} python setup.py  \
-    bdist_wheel                 \
-    sdist
+    bdist_wheel_grpc_custom
 
-# The bdist_wheel_grpc_custom command is finicky about command output ordering
-# and thus ought to be run in a shell command separate of others.
 GRPC_PYTHON_USE_CUSTOM_BDIST=0  \
 GRPC_PYTHON_BUILD_WITH_CYTHON=1 \
 ${SETARCH_CMD} python setup.py  \
-    bdist_wheel_grpc_custom
+    bdist_wheel                 \
+    sdist
 
 mkdir -p artifacts