diff --git a/tools/internal_ci/linux/grpc_distribtests_python.sh b/tools/internal_ci/linux/grpc_distribtests_python.sh
index aef918118ff..7192fcc707b 100755
--- a/tools/internal_ci/linux/grpc_distribtests_python.sh
+++ b/tools/internal_ci/linux/grpc_distribtests_python.sh
@@ -35,7 +35,7 @@ cp -r artifacts/* input_artifacts/ || true
 rm -rf artifacts_from_build_artifacts_step
 mv artifacts artifacts_from_build_artifacts_step || true
 
-# This step mostly just copies artifacts from input_artifacts (but it also does some wheel stripping)
+# This step only copies artifacts from input_artifacts
 tools/run_tests/task_runner.py -f package linux python -x build_packages/sponge_log.xml || FAILED="true"
 
 # the next step expects to find the artifacts from the previous step in the "input_artifacts" folder.
diff --git a/tools/run_tests/artifacts/build_artifact_python.sh b/tools/run_tests/artifacts/build_artifact_python.sh
index 8677079f0ad..8f18eb38d8b 100755
--- a/tools/run_tests/artifacts/build_artifact_python.sh
+++ b/tools/run_tests/artifacts/build_artifact_python.sh
@@ -126,20 +126,41 @@ ${SETARCH_CMD} "${PYTHON}" tools/distrib/python/grpcio_tools/setup.py sdist
 # shellcheck disable=SC2086
 ${SETARCH_CMD} "${PYTHON}" tools/distrib/python/grpcio_tools/setup.py bdist_wheel $WHEEL_PLAT_NAME_FLAG
 
+# run twine check before auditwheel, because auditwheel puts the repaired wheels into
+# the artifacts output dir.
+if [ "$GRPC_SKIP_TWINE_CHECK" == "" ]
+then
+  # Ensure the generated artifacts are valid.
+  # TODO(jtattermusch): avoid the need for always re-installing virtualenv and twine
+  "${PYTHON}" -m pip install virtualenv
+  "${PYTHON}" -m virtualenv venv || { "${PYTHON}" -m pip install virtualenv==16.7.9 && "${PYTHON}" -m virtualenv venv; }
+  venv/bin/python -m pip install "twine<=2.0"
+  venv/bin/python -m twine check dist/* tools/distrib/python/grpcio_tools/dist/*
+  rm -rf venv/
+fi
+
 if [ "$GRPC_RUN_AUDITWHEEL_REPAIR" != "" ]
 then
   for wheel in dist/*.whl; do
     "${AUDITWHEEL}" show "$wheel" | tee /dev/stderr |  grep -E -w "$AUDITWHEEL_PLAT"
-    "${AUDITWHEEL}" repair "$wheel" -w "$ARTIFACT_DIR"
+    "${AUDITWHEEL}" repair "$wheel" --strip --wheel-dir "$ARTIFACT_DIR"
     rm "$wheel"
   done
   for wheel in tools/distrib/python/grpcio_tools/dist/*.whl; do
     "${AUDITWHEEL}" show "$wheel" | tee /dev/stderr |  grep -E -w "$AUDITWHEEL_PLAT"
-    "${AUDITWHEEL}" repair "$wheel" -w "$ARTIFACT_DIR"
+    "${AUDITWHEEL}" repair "$wheel" --strip --wheel-dir "$ARTIFACT_DIR"
     rm "$wheel"
   done
+else
+  cp -r dist/*.whl "$ARTIFACT_DIR"
+  cp -r tools/distrib/python/grpcio_tools/dist/*.whl "$ARTIFACT_DIR"
 fi
 
+# grpcio and grpcio-tools wheels have already been copied to artifact_dir
+# by "auditwheel repair", now copy the .tar.gz source archives as well.
+cp -r dist/*.tar.gz "$ARTIFACT_DIR"
+cp -r tools/distrib/python/grpcio_tools/dist/*.tar.gz "$ARTIFACT_DIR"
+
 # We need to use the built grpcio-tools/grpcio to compile the health proto
 # Wheels are not supported by setup_requires/dependency_links, so we
 # manually install the dependency.  Note we should only do this if we
@@ -200,16 +221,3 @@ then
       sdist bdist_wheel
   cp -r src/python/grpcio_admin/dist/* "$ARTIFACT_DIR"
 fi
-
-if [ "$GRPC_SKIP_TWINE_CHECK" == "" ]
-then
-  # Ensure the generated artifacts are valid.
-  "${PYTHON}" -m pip install virtualenv
-  "${PYTHON}" -m virtualenv venv || { "${PYTHON}" -m pip install virtualenv==16.7.9 && "${PYTHON}" -m virtualenv venv; }
-  venv/bin/python -m pip install "twine<=2.0"
-  venv/bin/python -m twine check dist/* tools/distrib/python/grpcio_tools/dist/*
-  rm -rf venv/
-fi
-
-cp -r dist/* "$ARTIFACT_DIR"
-cp -r tools/distrib/python/grpcio_tools/dist/* "$ARTIFACT_DIR"
diff --git a/tools/run_tests/artifacts/build_package_python.sh b/tools/run_tests/artifacts/build_package_python.sh
index 9189cfa651b..29801a5b867 100755
--- a/tools/run_tests/artifacts/build_package_python.sh
+++ b/tools/run_tests/artifacts/build_package_python.sh
@@ -23,25 +23,6 @@ mkdir -p artifacts/
 # and we only collect them here to deliver them to the distribtest phase.
 cp -r "${EXTERNAL_GIT_ROOT}"/input_artifacts/python_*/* artifacts/ || true
 
-export PYTHON=${PYTHON:-python}
-
-strip_binary_wheel() {
-    WHEEL_PATH="$1"
-    TEMP_WHEEL_DIR=$(mktemp -d)
-    ${PYTHON} -m wheel unpack "$WHEEL_PATH" -d "$TEMP_WHEEL_DIR"
-    find "$TEMP_WHEEL_DIR" -name "_protoc_compiler*.so" -exec strip --strip-debug {} ";"
-    find "$TEMP_WHEEL_DIR" -name "cygrpc*.so" -exec strip --strip-debug {} ";"
-
-    DISTRIBUTION_NAME=$(basename "$WHEEL_PATH" | cut -d '-' -f 1)
-    VERSION=$(basename "$WHEEL_PATH" | cut -d '-' -f 2)
-    ${PYTHON} -m wheel pack "$TEMP_WHEEL_DIR/$DISTRIBUTION_NAME-$VERSION" -d "$TEMP_WHEEL_DIR"
-    mv "${TEMP_WHEEL_DIR}"/*.whl "$WHEEL_PATH"
-}
-
-for wheel in artifacts/*.whl; do
-    strip_binary_wheel "$wheel"
-done
-
 # TODO: all the artifact builder configurations generate a grpcio-VERSION.tar.gz
 # source distribution package, and only one of them will end up
 # in the artifacts/ directory. They should be all equivalent though.