diff --git a/CHANGELOG.md b/CHANGELOG.md
index f87b81b8f..22865fbac 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,7 @@
 
 # Master
 
+- For repeat builds, also manage the installed versions of setuptools/wheel, rather than just that of pip (#1007).
 - Install an explicit version of wheel rather than the latest release at the time (#1007).
 - Output the installed version of pip, setuptools and wheel in the build log (#1007).
 - Install setuptools from PyPI rather than a vendored copy (#1007).
diff --git a/bin/steps/python b/bin/steps/python
index 60564fc0c..88328fcbb 100755
--- a/bin/steps/python
+++ b/bin/steps/python
@@ -131,7 +131,6 @@ if [ ! "$SKIP_INSTALL" ]; then
   # Record for future reference.
   echo "$PYTHON_VERSION" > .heroku/python-version
   echo "$STACK" > .heroku/python-stack
-  FRESH_PYTHON=true
 
   hash -r
 fi
@@ -162,13 +161,9 @@ if ! curl -s "${GETPIP_URL}" -o "$GETPIP_PY" &> /dev/null; then
     exit 1
 fi
 
-# If a new Python has been installed or Pip isn't up to date:
-if [ "$FRESH_PYTHON" ] || [[ ! $(pip --version) == *${PIP_VERSION}* ]]; then
+puts-step "Installing pip ${PIP_VERSION}, setuptools ${SETUPTOOLS_VERSION} and wheel ${WHEEL_VERSION}"
 
-  puts-step "Installing pip ${PIP_VERSION}, setuptools ${SETUPTOOLS_VERSION} and wheel ${WHEEL_VERSION}"
-
-  /app/.heroku/python/bin/python "$GETPIP_PY" pip=="${PIP_VERSION}" "setuptools==${SETUPTOOLS_VERSION}" "wheel==${WHEEL_VERSION}" &> /dev/null
-fi
+/app/.heroku/python/bin/python "$GETPIP_PY" pip=="${PIP_VERSION}" "setuptools==${SETUPTOOLS_VERSION}" "wheel==${WHEEL_VERSION}" &> /dev/null
 
 set -e
 hash -r