diff --git a/.github/workflows/cd.yml b/.github/workflows/cd.yml
index 6e0e4cd..b088283 100644
--- a/.github/workflows/cd.yml
+++ b/.github/workflows/cd.yml
@@ -27,7 +27,18 @@ jobs:
         with:
           fetch-depth: 0
 
-      - uses: hynek/build-and-inspect-python-package@v2
+      # NOTE: For simplicity, we only want to ship the sdist, and this action doesn't
+      # support turning of wheels
+      # - uses: hynek/build-and-inspect-python-package@v2
+      - name: Build sdist
+        run: |
+          python -m pip install --upgrade build
+          python -m build --sdist .
+
+      - uses: actions/upload-artifact@v4
+        with:
+          name: Packages
+          path: dist/*
 
   # Upload to Test PyPI on every commit on main.
   test-publish:
diff --git a/pyproject.toml b/pyproject.toml
index 29d74a0..067acf2 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -2,7 +2,6 @@
 requires = [
     "setuptools>=64",
     "setuptools_scm>=8",
-    "wheel",
     "numpy",
     "scipy",
     "cython",