diff --git a/scripts/build.sh b/scripts/build.sh
index 97af69babc8..c66e234af05 100755
--- a/scripts/build.sh
+++ b/scripts/build.sh
@@ -9,16 +9,29 @@ set -ev
 python3 -m pip install --upgrade pip setuptools wheel
 
 BASEDIR=$(dirname $(readlink -f $(dirname $0)))
+DISTDIR=dist
 
 (
   cd $BASEDIR
-  mkdir -p dist
-  rm -rf dist/*
+  mkdir -p $DISTDIR
+  rm -r $DISTDIR/*
 
  for d in opentelemetry-api/ opentelemetry-sdk/ ext/*/ ; do
    (
+     echo "building $d"
      cd "$d"
-     python3 setup.py --verbose bdist_wheel --dist-dir "$BASEDIR/dist/"
+     # Some ext directories (such as docker tests) are not intended to be
+     # packaged. Verify the intent by looking for a setup.py.
+     if [ -f setup.py ]; then
+      python3 setup.py sdist --dist-dir "$BASEDIR/dist/" clean --all
+     fi
    )
  done
+ # Build a wheel for each source distribution
+ (
+   cd $DISTDIR
+   for x in *.tar.gz ; do
+     pip wheel --no-deps $x
+   done
+ )
 )