diff --git a/.github/workflows/build-image.yml b/.github/workflows/build-image.yml
index aa45b6d..3f135ac 100644
--- a/.github/workflows/build-image.yml
+++ b/.github/workflows/build-image.yml
@@ -2,7 +2,6 @@ name: build-docker-image
 
 on:
   workflow_dispatch:
-  pull_request:
   push:
     branches:
       - main
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index ea24e1d..8e66789 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -3,28 +3,29 @@ name: continuous-integration
 on: [push, pull_request]
 
 jobs:
-    test-package:
-        runs-on: ubuntu-latest
-        strategy:
-            matrix:
-                python-version: ['3.10', '3.11', '3.12']
+  test-package:
+    runs-on: ubuntu-latest
+    container: ghcr.io/${{ github.repository }}/ci-image:latest
+    strategy:
+      matrix:
+        python-version: ["3.10", "3.11", "3.12"]
 
-        steps:
-            - name: Check out repository
-              uses: actions/checkout@v4
+    steps:
+      - name: Check out repository
+        uses: actions/checkout@v4
 
-            - name: Set up Python
-              uses: actions/setup-python@v4
-              with:
-                  python-version: ${{ matrix.python-version }}
+      - name: Set up Python
+        uses: actions/setup-python@v4
+        with:
+          python-version: ${{ matrix.python-version }}
 
-            - name: Install package and its dependencies
-              run: pip install -e .[dev]
+      - name: Install package and its dependencies
+        run: python3 -m pip install -e .[dev]
 
-            - name: Run pytest
-              run: pytest -v --cov --cov-report json
+      - name: Run pytest
+        run: pytest -v --cov --cov-report json
 
-            - name: Upload coverage report
-              uses: codecov/codecov-action@v3
-              with:
-                  flags: python-${{ matrix.python-version }}
+      - name: Upload coverage report
+        uses: codecov/codecov-action@v3
+        with:
+          flags: python-${{ matrix.python-version }}
diff --git a/Dockerfile b/Dockerfile
index 098e53b..ff6d738 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -1,6 +1,4 @@
-# Use Ubuntu as the base image
-FROM ubuntu:latest AS base
+FROM alpine:latest AS base
 
-# Install build-essential, cmake, and OpenBLAS
-RUN apt-get update && \
-    apt-get install -y build-essential cmake libopenblas-dev
+RUN apk update && \
+    apk add --no-cache build-base cmake openblas-dev python3
diff --git a/cleedpy/cleed/CMakeLists.txt b/cleedpy/cleed/CMakeLists.txt
index bb11827..1139401 100644
--- a/cleedpy/cleed/CMakeLists.txt
+++ b/cleedpy/cleed/CMakeLists.txt
@@ -6,8 +6,8 @@ set(CMAKE_C_STANDARD 90)
 set(CMAKE_C_STANDARD_REQUIRED True)
 
 # Set the output directories
-set(CMAKE_LIBRARY_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/lib)
-set(CMAKE_RUNTIME_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/bin)
+set(CMAKE_LIBRARY_OUTPUT_DIRECTORY ${CMAKE_SOURCE_DIR}/lib)
+set(CMAKE_RUNTIME_OUTPUT_DIRECTORY ${CMAKE_SOURCE_DIR}/bin)
 
 # Where to find CMake modules
 list(APPEND CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
diff --git a/cleedpy/interface/cleed.py b/cleedpy/interface/cleed.py
index c3ba4eb..1e6dfe0 100644
--- a/cleedpy/interface/cleed.py
+++ b/cleedpy/interface/cleed.py
@@ -1,7 +1,8 @@
 import math
-from ctypes import POINTER, Structure, c_char_p, c_double, c_int, cdll
+import pathlib as pl
+import platform
+from ctypes import CDLL, POINTER, Structure, c_char_p, c_double, c_int, cdll
 from dataclasses import dataclass
-from pathlib import Path
 
 from ..config import (
     AtomParametersStructured,
@@ -188,9 +189,29 @@ def generate_crystal_structure(inp: AtomParametersVariants) -> Crystal:
             raise ValueError("Not implemented")
 
 
-def call_cleed():
-    path = Path(__file__).parent.parent / "cleed" / "build" / "lib" / "libcleed.dylib"
-    lib = cdll.LoadLibrary(str(path))
+def get_cleed_lib() -> CDLL:
+    lib_path = pl.Path(__file__).parent.parent / "cleed" / "lib"
+
+    lib_exts = {
+        "Windows": ".dll",
+        "Darwin": ".dylib",
+        "Linux": ".so",
+    }
+
+    try:
+        cleed_lib = (
+            (lib_path / "libcleed").with_suffix(lib_exts[platform.system()]).as_posix()
+        )
+    except KeyError as err:
+        raise ValueError(
+            f"Platform {platform.system()} not supported by cleedpy"
+        ) from err
+
+    return cdll.LoadLibrary(cleed_lib)
+
+
+def call_cleed() -> None:
+    lib = get_cleed_lib()
 
     lib.my_test_function.argtypes = [c_int, c_int, POINTER(Crystal)]
     lib.my_test_function.restype = c_int
diff --git a/pyproject.toml b/pyproject.toml
index aa77348..b1d7c48 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,5 +1,5 @@
 [build-system]
-requires = ["setuptools>=61.2"]
+requires = ["setuptools>=61.2", "cmake>=3.5"]
 build-backend = "setuptools.build_meta"
 
 
diff --git a/setup.py b/setup.py
new file mode 100644
index 0000000..543f31a
--- /dev/null
+++ b/setup.py
@@ -0,0 +1,77 @@
+import os
+import pathlib as pl
+import platform
+import subprocess
+import sys
+
+from setuptools import Extension, setup
+from setuptools.command.build_ext import build_ext
+
+
+class CMakeExtension(Extension):
+    def __init__(self, name, source_dir=""):
+        Extension.__init__(self, name, sources=[])
+        self.source_dir = pl.Path(source_dir).absolute()
+
+
+class CMakeBuild(build_ext):
+    def run(self):
+        try:
+            subprocess.check_output(["cmake", "--version"])
+        except subprocess.CalledProcessError as err:
+            raise RuntimeError(
+                "CMake must be installed to build the following extensions: "
+                + ", ".join(e.name for e in self.extensions)
+            ) from err
+
+        for ext in self.extensions:
+            self.build_extension(ext)
+
+    def build_extension(self, ext: CMakeExtension):
+        ext_dir = pl.Path(self.get_ext_fullpath(ext.name)).parent.absolute()
+
+        cmake_args = ["-DPYTHON_EXECUTABLE=" + sys.executable]
+
+        cfg = "Debug" if self.debug else "Release"
+        build_args = ["--config", cfg]
+
+        if platform.system() == "Windows":
+            cmake_args += [f"-DCMAKE_LIBRARY_OUTPUT_DIRECTORY_{cfg.upper()}={ext_dir}"]
+            if sys.maxsize > 2**32:
+                # We are on a Win 64-bit system
+                cmake_args += ["-A", "x64"]
+            build_args += ["--", "/m"]
+        else:
+            # These flags are passed as-is to the underlying build tool (make)
+            build_args += ["--", "-j2"]
+
+        env = os.environ.copy()
+        env["CXXFLAGS"] = '{} -DVERSION_INFO="{}"'.format(
+            env.get("CXXFLAGS", ""), self.distribution.get_version()
+        )
+
+        build_dir = pl.Path(self.build_temp)
+        build_dir.mkdir(parents=True, exist_ok=True)
+
+        try:
+            subprocess.check_call(
+                ["cmake", "-S", ext.source_dir.as_posix(), "-B", "."] + cmake_args,
+                cwd=build_dir,
+                env=env,
+            )
+            subprocess.check_call(["cmake", "--build", "."] + build_args, cwd=build_dir)
+        except subprocess.CalledProcessError as err:
+            raise RuntimeError(f"CMake error: {err}") from err
+
+
+setup(
+    name="cleedpy",
+    ext_modules=[
+        CMakeExtension(
+            "cleed", (pl.Path(__file__).parent / "cleedpy" / "cleed").as_posix()
+        )
+    ],
+    cmdclass={"build_ext": CMakeBuild},
+    # The following includes *any* library file found in the package directory
+    package_data={"cleedpy": ["**/*.dylib", "**/*.so", "**/*.dll"]},
+)