diff --git a/Dockerfile b/Dockerfile
index 15d6c2b..1640791 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -1,10 +1,19 @@
-FROM --platform=$TARGETPLATFORM python:3.11-slim
+# Split out the wheel build into the non-slim image
+# See https://github.com/docker-library/python/issues/869
+FROM python:3.12 AS build
+COPY requirements.txt ./
+RUN --mount=type=cache,target=/var/cache/buildkit/pip \
+    pip wheel --wheel-dir /wheels -r requirements.txt
+
+FROM python:3.12-slim
 LABEL org.opencontainers.image.source=https://github.com/mdiluz/matchy
 LABEL org.opencontainers.image.description="Matchy matches matchees"
 LABEL org.opencontainers.image.licenses=Unlicense
 
-WORKDIR /usr/src/app
 COPY requirements.txt ./
-RUN pip install --no-cache-dir -r requirements.txt
+COPY --from=build /wheels /wheels
+RUN --mount=type=cache,target=/var/cache/buildkit/pip \
+    pip install --find-links /wheels --no-index -r requirements.txt
+
 COPY . .
 CMD ["python", "py/matchy.py"]
\ No newline at end of file