diff --git a/Dockerfile.package b/Dockerfile.package
new file mode 100644
index 0000000..7e0c7eb
--- /dev/null
+++ b/Dockerfile.package
@@ -0,0 +1 @@
+FROM quay.io/pypa/manylinux_2_28_x86_64
diff --git a/Dockerfile.pkg1 b/Dockerfile.pkg1
deleted file mode 100644
index 286fd14..0000000
--- a/Dockerfile.pkg1
+++ /dev/null
@@ -1,27 +0,0 @@
-FROM ubuntu:20.04
-
-RUN apt update && \
-    DEBIAN_FRONTEND=noninteractive apt install -y python3 python3.8-venv python3.9 python3.9-venv python3-setuptools python3-pip git build-essential cmake wget python3.9-dev
-RUN cd /tmp \
-    && wget https://github.com/Kitware/CMake/releases/download/v3.30.4/cmake-3.30.4-linux-x86_64.tar.gz \
-    && tar -xf cmake-3.30.4-linux-x86_64.tar.gz \
-    && cp -r cmake-3.30.4-linux-x86_64/bin/* /usr/local/bin/ \
-    && cp -r cmake-3.30.4-linux-x86_64/man/* /usr/local/man/ \
-    && cp -r cmake-3.30.4-linux-x86_64/share/* /usr/local/share/
-
-COPY . /grgl_src
-
-ENV PATH="/grgl_src/Env38/bin:$PATH"
-# Build the Python 3.8 wheel
-RUN cd /grgl_src \
-    && python3.8 -m venv Env38 \
-    && pip3 install wheel \
-    && GRGL_GSL=1 GRGL_BGEN=1 python setup.py bdist_wheel
-ENV PATH="/grgl_src/Env39/bin:$PATH"
-# Build the Python 3.9 wheel
-RUN cd /grgl_src \
-    && python3.9 -m venv Env39 \
-    && pip3 install wheel \
-    && GRGL_GSL=1 GRGL_BGEN=1 python setup.py bdist_wheel
-# Copy to an easily accesible location
-RUN mkdir /output && cp /grgl_src/dist/*.whl /output/
diff --git a/Dockerfile.pkg2 b/Dockerfile.pkg2
deleted file mode 100644
index 4f03c35..0000000
--- a/Dockerfile.pkg2
+++ /dev/null
@@ -1,21 +0,0 @@
-FROM ubuntu:22.04
-
-RUN apt update && \
-    DEBIAN_FRONTEND=noninteractive apt install -y python3.10 python3.10-venv python3.10-dev python3.11 python3.11-venv python3.11-dev python3-setuptools python3-pip git build-essential cmake wget 
-
-COPY . /grgl_src
-
-ENV PATH="/grgl_src/Env310/bin:$PATH"
-# Build the Python 3.10 wheel
-RUN cd /grgl_src \
-    && python3.10 -m venv Env310 \
-    && pip3 install wheel \
-    && GRGL_GSL=1 GRGL_BGEN=1 python setup.py bdist_wheel
-ENV PATH="/grgl_src/Env311/bin:$PATH"
-# Build the Python 3.11 wheel
-RUN cd /grgl_src \
-    && python3.11 -m venv Env311 \
-    && pip3 install wheel \
-    && GRGL_GSL=1 GRGL_BGEN=1 python setup.py bdist_wheel
-# Copy to an easily accesible location
-RUN mkdir /output && cp /grgl_src/dist/*.whl /output/
diff --git a/RELEASING.md b/RELEASING.md
index c39e4f5..9b28a76 100644
--- a/RELEASING.md
+++ b/RELEASING.md
@@ -16,29 +16,28 @@ Steps:
 
 ## Packaging for PyPi
 
-Build the package distributions for PyPi. We build a source dist and then Linux binary distributions for recent Python versions.
+Build the package distributions for PyPi. We build a source dist and then Linux binary distributions for recent Python versions. The container is based on the [manylinux](https://github.com/pypa/manylinux) project.
 
 ```
 # Remove dist/ to start fresh
 rm -rf dist
 
-# Build the source distribution (for MacOS, mostly)
-python setup.py sdist
+# Build the container based on the manylinux project
+docker build . -f Dockerfile.pkg -t grgl_pkg:latest
 
-# Build the Python3.8 and Python3.9 packages on an older Docker image
-docker build . -f Dockerfile.pkg1 -t grgl_pkg1:latest
-docker run -v $PWD/dist:/dist -it grgl_pkg1:latest bash -c "cp /output/*.whl /dist/"
-
-# Build the Python3.10+ packages on a newer Docker image
-docker build . -f Dockerfile.pkg2 -t grgl_pkg2:latest
-docker run -v $PWD/dist:/dist -it grgl_pkg2:latest bash -c "cp /output/*.whl /dist/"
+# Run the packaging inside the container
+docker run -v $PWD:/io -it grgl_pkg:latest /io/package.sh
 
 # Fix file permissions from Docker
-sudo chown ddehaas dist/*.whl
-sudo chgrp ddehaas dist/*.whl
+sudo chown -R ddehaas dist/
+sudo chgrp -R ddehaas dist/
+
+# Copy the source wheel to wheelhouse
+cp ./dist/*.tar.gz ./dist/wheelhouse/
+
 ```
 
-To upload to PyPi, ensure that your dist directory is clean (only has the packages you _just_ built), then upload via twine:
+To upload to PyPi:
 ```
-python3 -m twine upload dist/*
+python3 -m twine upload dist/wheelhouse/*
 ```
diff --git a/package.sh b/package.sh
new file mode 100755
index 0000000..36ccba1
--- /dev/null
+++ b/package.sh
@@ -0,0 +1,26 @@
+#!/bin/bash
+
+set -ev
+
+cd /io 
+
+# Build the source distribution
+/opt/python/cp38-cp38/bin/python setup.py sdist
+
+echo "Building for Python 3.8"
+GRGL_GSL=1 GRGL_BGEN=1 /opt/python/cp38-cp38/bin/python setup.py bdist_wheel
+echo "Building for Python 3.9"
+GRGL_GSL=1 GRGL_BGEN=1 /opt/python/cp39-cp39/bin/python setup.py bdist_wheel
+echo "Building for Python 3.10"
+GRGL_GSL=1 GRGL_BGEN=1 /opt/python/cp310-cp310/bin/python setup.py bdist_wheel
+echo "Building for Python 3.11"
+GRGL_GSL=1 GRGL_BGEN=1 /opt/python/cp311-cp311/bin/python setup.py bdist_wheel
+echo "Building for Python 3.12"
+GRGL_GSL=1 GRGL_BGEN=1 /opt/python/cp312-cp312/bin/python setup.py bdist_wheel
+
+cd /io/dist
+auditwheel repair --plat manylinux_2_24_x86_64 pygrgl-1.1-cp38-cp38-linux_x86_64.whl
+auditwheel repair --plat manylinux_2_24_x86_64 pygrgl-1.1-cp39-cp39-linux_x86_64.whl
+auditwheel repair --plat manylinux_2_24_x86_64 pygrgl-1.1-cp310-cp310-linux_x86_64.whl
+auditwheel repair --plat manylinux_2_24_x86_64 pygrgl-1.1-cp311-cp311-linux_x86_64.whl
+auditwheel repair --plat manylinux_2_24_x86_64 pygrgl-1.1-cp312-cp312-linux_x86_64.whl