diff --git a/.github/workflows/rust.yml b/.github/workflows/rust.yml
index 44025ad..a629bc0 100644
--- a/.github/workflows/rust.yml
+++ b/.github/workflows/rust.yml
@@ -73,8 +73,19 @@ jobs:
 
     - name: Verify cargo publish includes all files needed to build
       run: |
-        cargo package --list -p chrono-tz
-        cargo publish --dry-run -p chrono-tz
+        cargo vendor
+        cargo package -p chrono-tz-build
+        cargo package -p chrono-tz --no-verify
+        for crate in target/package/*.crate
+        do
+          name=$(basename "$crate" .crate)
+          tar xvfz "$crate" -C vendor/
+          # Crates in the vendor directory require a checksum file, but it
+          # doesn't matter if it is empty.
+          echo '{"files":{}}' > vendor/$name/.cargo-checksum.json
+        done
+        cargo package --config "source.vendored-sources.directory = 'vendor'" \
+           --config "source.crates-io.replace-with = 'vendored-sources'"
 
   lint:
     runs-on: ubuntu-latest