diff --git a/Dockerfile b/Dockerfile
index 49dd47f3..94c234d7 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -1,4 +1,75 @@
-FROM python:3.11-slim-buster
+#
+# Static build of `curl` with both HTTP2 and HTTP3 support.
+#
+# This was adapted from stunnel's script:
+# https://github.com/stunnel/static-curl/blob/f8a20698bd39b6/build.sh
+#
+FROM alpine AS buildcurl
+
+RUN apk update && \
+    apk add \
+        build-base clang automake cmake autoconf libtool linux-headers git \
+        binutils cunit-dev
+
+ENV PREFIX=/opt/curl
+ENV PKG_CONFIG_PATH=$PREFIX/lib/pkgconfig:$PREFIX/lib64/pkgconfig:$PKG_CONFIG_PATH
+
+RUN git clone --depth 1 -b openssl-3.0.8+quic https://github.com/quictls/openssl && \
+    cd openssl && \
+    mkdir -p "${PREFIX}/lib/" "${PREFIX}/lib64/" "${PREFIX}/include/" && \
+    ./config -fPIC --prefix="${PREFIX}" \
+        threads no-shared enable-tls1_3 && \
+    make -j $(nproc) && \
+    make install_sw && \
+    cd ..
+
+RUN git clone -b v0.11.0 https://github.com/ngtcp2/nghttp3 && \
+    cd nghttp3 && \
+    autoreconf -i --force && \
+    PKG_CONFIG="pkg-config --static --with-path=$PREFIX/lib/pkgconfig" \
+        ./configure --prefix="${PREFIX}" --enable-static --enable-shared=no --enable-lib-only && \
+    make -j $(nproc) && \
+    make install && \
+    cd ..
+
+RUN git clone -b v0.15.0 https://github.com/ngtcp2/ngtcp2 && \
+    cd ngtcp2 && \
+    autoreconf -i --force && \
+    PKG_CONFIG="pkg-config --static --with-path=${PREFIX}/lib/pkgconfig:${PREFIX}/lib64/pkgconfig" \
+        ./configure --prefix="${PREFIX}" --enable-static --with-openssl=${PREFIX} \
+            --with-libnghttp3=${PREFIX} --enable-lib-only --enable-shared=no && \
+    make -j $(nproc) check && \
+    make install && \
+    cd ..
+
+RUN git clone https://github.com/nghttp2/nghttp2 && \
+    cd nghttp2 && \
+    autoreconf -i --force && \
+    PKG_CONFIG="pkg-config --static --with-path=$PREFIX/lib/pkgconfig" \
+        ./configure --prefix="${PREFIX}" --enable-static --enable-http3 \
+            --enable-lib-only --enable-shared=no && \
+    make -j $(nproc) check && \
+    make install && \
+    cd ..
+
+RUN git clone https://github.com/curl/curl && \
+    cd curl && \
+    autoreconf -i --force && \
+    PKG_CONFIG="pkg-config --static" \
+        ./configure --prefix="${PREFIX}" \
+            --disable-shared --enable-static \
+             --with-openssl \
+             --with-nghttp2 --with-nghttp3 --with-ngtcp2 && \
+    make -j $(nproc) V=1 LDFLAGS="-L${PREFIX}/lib -L${PREFIX}/lib64 -static -all-static" CFLAGS="-O3" && \
+    make install && \
+    # We now have a static binary of curl at `${PREFIX}/bin/curl`
+    cd ..
+
+
+#
+# Production container.
+#
+FROM python:3.11-slim-buster AS production
 
 WORKDIR /app
 
@@ -6,19 +77,14 @@ RUN groupadd --gid 10001 app \
     && useradd -m -g app --uid 10001 -s /usr/sbin/nologin app
 
 RUN apt-get update && \
-    apt-get install --yes --no-install-recommends wget build-essential libssl-dev && \
+    apt-get install --yes --no-install-recommends build-essential && \
     pip install --progress-bar=off -U pip && \
     pip install poetry && \
-    # curl with http3 support
-    wget https://curl.se/download/curl-8.1.1.tar.gz && \
-    tar -xvf curl-*.tar.gz && cd curl-* && \
-    ./configure --with-openssl --disable-shared && make && make install && \
-    cd .. && \
-    # cleanup
     apt-get -q --yes autoremove && \
     apt-get clean && \
     rm -rf /root/.cache
 
+COPY --from=buildcurl /opt/curl/bin/curl /usr/local/bin/curl
 COPY ./pyproject.toml /app
 COPY ./poetry.lock /app