diff --git a/scripts/check-api-compatibility.sh b/scripts/check-api-compatibility.sh
index 187df5ab4c785..3cc97cdca81e7 100755
--- a/scripts/check-api-compatibility.sh
+++ b/scripts/check-api-compatibility.sh
@@ -14,7 +14,7 @@ package_name() {
 # Doesn't use 'npm view' as that is slow. Direct curl'ing npmjs is better
 package_exists_on_npm() {
     pkg=$1
-    ver=${2:-} # optional
+    ver=$2 # optional
     curl -I 2>/dev/null https://registry.npmjs.org/$pkg/$ver | head -n 1 | grep 200 >/dev/null
 }
 
@@ -32,13 +32,10 @@ jsii_package_dirs=$(list_jsii_packages)
 
 #----------------------------------------------------------------------
 
-# dirs_for_existing_pkgs DIRECTORY VERSION
-#
-# Input a directory and a version, output the directory IF it exists on NPM at that version
+# Input a directory, output the directory IF it exists on NPM
 dirs_for_existing_pkgs() {
     local dir="$1"
-    local ver="$2"
-    if package_exists_on_npm $(package_name $dir) $ver; then
+    if package_exists_on_npm $(package_name $dir); then
         echo "$dir"
         echo -n "." >&2
     else
@@ -52,24 +49,30 @@ export -f dirs_for_existing_pkgs
 
 if ! ${SKIP_DOWNLOAD:-false}; then
     echo "Filtering on existing packages on NPM..." >&2
+    # In parallel
+    existing_pkg_dirs=$(echo "$jsii_package_dirs" | xargs -n1 -P4 -I {} bash -c 'dirs_for_existing_pkgs "$@"' _ {})
+    existing_names=$(echo "$existing_pkg_dirs" | xargs -n1 -P4 -I {} bash -c 'package_name "$@"' _ {})
+    echo " Done." >&2
 
     echo "Determining baseline version..." >&2
     version=$(node -p 'require("./scripts/resolve-version.js").version')
     echo "  Current version is $version." >&2
-    echo "Using version '$version' as the baseline..."
 
-    # Filter packages by existing at the target version
-    existing_pkg_dirs=$(echo "$jsii_package_dirs" | xargs -n1 -P4 -I {} bash -c 'dirs_for_existing_pkgs "$@" "'$version'"' _ {})
-    existing_names=$(echo "$existing_pkg_dirs" | xargs -n1 -P4 -I {} bash -c 'package_name "$@"' _ {})
-    install_versions=$(for name in $existing_names; do echo "${name}@${version}"; done)
-    echo " Done." >&2
+    if ! package_exists_on_npm aws-cdk $version; then
+        major_version=$(echo "$version" | sed -e 's/\..*//g')
+        echo "  Version $version does not exist in npm. Falling back to package major version ${major_version}" >&2
+        existing_names=$(echo "$existing_names" | sed -e "s/$/@$major_version/")
+    else
+        echo "Using version '$version' as the baseline..."
+        existing_names=$(echo "$existing_names" | sed -e "s/$/@$version/")
+    fi
 
     rm -rf $tmpdir
     mkdir -p $tmpdir
 
     echo "Installing from NPM..." >&2
     # use npm7 to automatically install peer dependencies
-    (cd $tmpdir && npx npm@^7.0.0 install --prefix $tmpdir $install_versions)
+    (cd $tmpdir && npx npm@^7.0.0 install --prefix $tmpdir $existing_names)
 fi
 
 #----------------------------------------------------------------------