diff --git a/repo2docker/buildpacks/python/freeze.bash b/repo2docker/buildpacks/python/freeze.bash
index bb614326..54bb30f9 100755
--- a/repo2docker/buildpacks/python/freeze.bash
+++ b/repo2docker/buildpacks/python/freeze.bash
@@ -17,23 +17,23 @@ cd $(dirname "$($realpath "$0")")
 function freeze-requirements {
     # Freeze a requirements file $2 into a frozen requirements file $3
     # Requires that a completely empty venv of appropriate version exist in $1
-    VENV_PATH="$1"
+    PYTHON_VERSION="$1"
     REQUIREMENTS_FILE="$2"
     FROZEN_FILE="$3"
+    if [[ $(echo ${PYTHON_VERSION} | cut -d. -f 1) == "2" ]]; then
+        VENV=virtualenv
+    else
+        VENV=venv
+    fi
 
-    ./${VENV_PATH}/bin/pip install --no-cache-dir -r ${REQUIREMENTS_FILE}
     echo "# AUTO GENERATED FROM ${REQUIREMENTS_FILE}, DO NOT MANUALLY MODIFY" > ${FROZEN_FILE}
     echo "# Frozen on $(date -u)" >> ${FROZEN_FILE}
-    ./${VENV_PATH}/bin/pip freeze | sort >> ${FROZEN_FILE}
+    docker run --rm -v $PWD:/python -it python:${PYTHON_VERSION} \
+        sh -c "
+            python -m $VENV /venv
+            /venv/bin/pip install -r /python/${REQUIREMENTS_FILE} &&
+            /venv/bin/pip freeze | sort --ignore-case >> /python/${FROZEN_FILE}"
 }
 
-rm -rf py3venv
-python3 -m venv py3venv
-freeze-requirements py3venv requirements.txt requirements.frozen.txt
-rm -rf py3venv
-
-
-rm -rf py2venv
-virtualenv -p python2 py2venv
-freeze-requirements py2venv requirements2.txt requirements2.frozen.txt
-rm -rf py2venv
+freeze-requirements 3.5 requirements.txt requirements.frozen.txt
+freeze-requirements 2.7 requirements2.txt requirements2.frozen.txt