diff --git a/.github/workflows/deploy_pypi.yml b/.github/workflows/deploy.yml
similarity index 95%
rename from .github/workflows/deploy_pypi.yml
rename to .github/workflows/deploy.yml
index 84434c9..7d4fa8f 100644
--- a/.github/workflows/deploy_pypi.yml
+++ b/.github/workflows/deploy.yml
@@ -3,7 +3,7 @@
 
 # SPDX-License-Identifier: BSD-3-Clause
 
-name: Publish package to Pypi
+name: Publish package to Pypi and to the current release
 
 on:
   release:
@@ -54,10 +54,10 @@ jobs:
       - name: Publish package distributions to PyPI
         uses: pypa/gh-action-pypi-publish@release/v1
 
-  github-release:
+  github-publish:
     name: Upload the release package to GitHub Release
     needs:
-      - pypi-publish
+      - release-packaging
     runs-on: ubuntu-22.04
     permissions:
       contents: write  # IMPORTANT: mandatory for making GitHub Releases
diff --git a/.github/workflows/tests.yaml b/.github/workflows/tests.yaml
index c8faf15..b90732f 100644
--- a/.github/workflows/tests.yaml
+++ b/.github/workflows/tests.yaml
@@ -3,12 +3,11 @@
 
 # SPDX-License-Identifier: BSD-3-Clause
 
-name: Execute code tests
+name: Test the code, doc building, and packaging
 
 on:
   push:
     branches: [ "main" ]
-    tags: ["*"]
   pull_request:
 
 permissions:
@@ -42,7 +41,6 @@ jobs:
           name: coverage-${{ matrix.pixi_environment }}-${{ matrix.os }}
           path: .coverage.${{ matrix.pixi_environment }}-${{ matrix.os }}
 
-
   merge-coverage:
     name: Merge the coverage reports from multiple coverages
     needs: tests
@@ -92,3 +90,30 @@ jobs:
         run: pixi run -e doc doc
       - name: Run doctests
         run: pixi run -e doc doctest
+
+  test-packaging:
+    name: Package the project into a distributable file
+    runs-on: ubuntu-22.04
+    steps:
+      - name: Checkout project
+        uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+      - name: Install python
+        uses: actions/setup-python@v5
+        with:
+          python-version: "3.10"
+      - name: Install build dependencies
+        run: |
+          pip install --upgrade pip
+          pip install build
+      - name: Package the project to the dist dir
+        run: python -m build
+      - name: Try installing from the new dists
+        run: pip install dist/*.whl
+      - name: Produce a GitHub actions artifact (the distributable package)
+        uses: actions/upload-artifact@v4
+        with:
+          name: dist
+          path: dist/
+          if-no-files-found: error