diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 7dd32cb..b6d2bdd 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -2,7 +2,7 @@ name: CI
 
 on:
   push:
-    branches: ["main"]
+    branches: ["**"] # For now, let's build all branches. Roll this back if it gets too slow or we exhaust our quota.
   pull_request:
     branches: ["**"] # * does not match '/'
   workflow_dispatch: # For manually triggering a build: https://docs.github.com/en/actions/writing-workflows/choosing-when-your-workflow-runs/events-that-trigger-workflows#workflow_dispatch
@@ -12,9 +12,10 @@ jobs:
     strategy:
       matrix:
         # We mainly care about hardware rather than OS
-        # macos-13 is x86. All later ones are arm64
+        # macos-13 is x86
+        # macos-latest is arm64
         # ubuntu-latest is x64
-        os: [macos-13, macos-latest, ubuntu-latest]
+        os: [ubuntu-latest, macos-latest, macos-13]
 
     runs-on: ${{ matrix.os }}
 
@@ -26,7 +27,6 @@ jobs:
       - uses: leanprover/lean-action@v1
       - name: Run tests
         run: lake exe klr
-
       # Run pytest
       - uses: actions/setup-python@v5
         with:
@@ -41,3 +41,18 @@ jobs:
         working-directory: ./interop
         run: |
           pytest
+      - name: Make a wheel
+        # https://github.com/pypa/cibuildwheel
+        # Hit this: https://github.com/pypa/cibuildwheel/discussions/1926
+        env:
+          # https://github.com/leanprover/lean4/pull/6631/files
+          MACOSX_DEPLOYMENT_TARGET: 99.0
+          CIBW_BUILD_VERBOSITY: 1
+          CIBW_SKIP: pp* # The build doesn't work on pypy:  auditwheel: error: cannot repair "/tmp/cibuildwheel/built_wheel/klr-0.0.3-cp38-cp38-linux_i686.whl" to "manylinux2014_i686" ABI because of the presence of too-recent versioned symbols. You'll need to compile the wheel on an older toolchain.
+        run: |
+          pip install cibuildwheel
+          bin/make-wheel
+      - uses: actions/upload-artifact@v4
+        with:
+          name: cibw-wheels-${{ matrix.os }}-${{ strategy.job-index }}
+          path: ./.wheel/wheelhouse/*.whl
diff --git a/.gitignore b/.gitignore
index 9acca94..2516042 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,6 +1,6 @@
-.lake/**
+\.lake/
 __pycache__/
 *.so
 *.dSYM
-/.vscode/
-.wheel/
+.vscode/
+/.wheel/
diff --git a/bin/make-wheel b/bin/make-wheel
index ead4f3a..b49f339 100755
--- a/bin/make-wheel
+++ b/bin/make-wheel
@@ -3,20 +3,31 @@ set -e -u -o pipefail
 trap "kill 0" SIGINT SIGTERM
 
 ROOT=$(dirname $(dirname $(readlink -f $0)))
-WHEEL_DIR=$ROOT/.wheel/klr
+WHEEL_DIR=$ROOT/.wheel/
+PYTHON_DIR=$ROOT/interop
 rm -rf $WHEEL_DIR
-mkdir -p $WHEEL_DIR/klr/bin
+mkdir -p $WHEEL_DIR/{klr,bin}
 lake build
-cp $ROOT/.lake/build/bin/klr $WHEEL_DIR/klr/bin/klr
-cp -R $ROOT/interop/nki $WHEEL_DIR/klr/nki
-cp -R $ROOT/interop/klr $WHEEL_DIR/klr/klr
+
+# Get klr binary
+cp .lake/build/bin/klr $WHEEL_DIR/bin/klr
+
+# Get Python packages
+cp -R $PYTHON_DIR/* $WHEEL_DIR
 cp $ROOT/LICENSE $WHEEL_DIR
-cp $ROOT/interop/README.md $WHEEL_DIR
-cp $ROOT/interop/pyproject.toml $WHEEL_DIR
-cp $ROOT/interop/MANIFEST.in $WHEEL_DIR
 
 cd $WHEEL_DIR
-python -m build
+
+if [ -z "${GITHUB_RUN_ID+x}" ]; then
+  echo "Building wheel locally"
+  python -m build
+else
+  # https://github.com/pypa/cibuildwheel
+  # NB: I could never get this to run on my mac locally. I got it to
+  # work on linux with no trouble.
+  echo "Building wheel via GitHub Actions"
+  python -m cibuildwheel --output-dir ./wheelhouse
+fi
 
 # To upload the wheel, with the proper token in ~/.pypirc, run
 #
diff --git a/interop/MANIFEST.in b/interop/MANIFEST.in
index 944d6af..04f0dcc 100644
--- a/interop/MANIFEST.in
+++ b/interop/MANIFEST.in
@@ -1 +1,2 @@
-include klr/bin/*
+# All files must be below the python project root
+include bin/klr
diff --git a/interop/README.md b/interop/README.md
index cdb2ee2..48f1a09 100644
--- a/interop/README.md
+++ b/interop/README.md
@@ -1,3 +1,4 @@
+
 Python bindings for KLR
 
 # Usage
@@ -19,3 +20,11 @@ We do this to remove a dependency on the `neuronxcc` Python package that does no
    require it since it's large and unnecessary.
 
 2. Automatically sync `nki` examples with the github examples
+
+# Notes
+
+I keep getting __pycache__ directories created in the source tree, even with
+
+    export PYTHONDONTWRITEBYTECODE=1
+
+This is annoying.
diff --git a/interop/klr/parser.py b/interop/klr/parser.py
index 56fa7d9..7fdc6c9 100644
--- a/interop/klr/parser.py
+++ b/interop/klr/parser.py
@@ -7,7 +7,6 @@
 import json
 import numpy as np
 import os
-import pathlib
 import subprocess
 import tempfile
 import types
@@ -16,10 +15,16 @@
 from textwrap import dedent
 from importlib.resources import files
 
+def up(f, n):
+  d = os.path.dirname(f)
+  for _ in range(n):
+    d = os.path.dirname(d)
+  return d
+
 
 def run_klr(infile, outfile):
   # For development, pick up the klr binary from the project dir
-  project_root = os.path.dirname(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
+  project_root = up(os.path.abspath(__file__), 2)
   bin = project_root + '/bin/klr'
   if not os.path.isfile(bin):
     # For regular pip users, pick up the klr from the wheel. While the type of `bin` here is
diff --git a/interop/noop.c b/interop/noop.c
new file mode 100644
index 0000000..d1adf6d
--- /dev/null
+++ b/interop/noop.c
@@ -0,0 +1,8 @@
+// A dummy file to trick Python's `build` into makeing an arch-specific wheel.
+
+#include <stdio.h>
+
+int main() {
+    printf("Hello, World!\n");
+    return 0;
+}
diff --git a/interop/pyproject.toml b/interop/pyproject.toml
index 65cec98..c16f65d 100644
--- a/interop/pyproject.toml
+++ b/interop/pyproject.toml
@@ -1,11 +1,17 @@
+# NB: All this setuptools stuff took about 1000 hours to figure out so never delete this.
+[build-system]
+#requires = ["setuptools>=61.0"]
+requires = ["setuptools"]
+build-backend = "setuptools.build_meta"
+
 [project]
 name = "klr"
-version = "0.0.2"
-description = "Intermediate langauge for tensor compilers"
+version = "0.0.3"
 authors = [
   {name = "Paul Govereau", email = "govereau@amazon.com"},
   {name = "Sean McLaughlin", email = "seanmcl@amazon.com"},
 ]
+description = "Intermediate langauge for tensor compilers"
 readme = "README.md"
 license = { file = "LICENSE" }
 keywords = ["trainium", "tpu", "pallas", "triton", "gpu"]
@@ -20,6 +26,10 @@ dependencies = [
   "ml_dtypes",
   "numpy",
 ]
+requires-python = ">= 3.8" # cibuildwheel can't seem to handle eariler versions
+
+[project.urls]
+Repository = "https://github.com/leanprover/KLR"
 
 [tool.pytest.ini_options]
 pythonpath = "." # Needed for tests to pass
@@ -27,5 +37,13 @@ testpaths = [
   "test",
 ]
 
-[project.urls]
-Repository = "https://github.com/leanprover/KLR"
+[tool.setuptools]
+packages = ["bin", "klr", "nki", 'nki.isa', 'nki.language'] # This field is tequired to have more than 1 top level packages (nki/klr). It's not beautiful but it works.
+
+# Build a fake C file to trick the `build` command to make an arch-specific wheel
+# We need this because we hide our `klr` Lean binary in the wheel but Python tools
+# don't know about it. I couldn't find another way to stop Python from generating
+# a generic `any` wheel.
+[[tool.setuptools.ext-modules]]
+name = "noop"
+sources = ["noop.c"]