diff --git a/docker/Dockerfile b/docker/Dockerfile
index 65b06ec..6780595 100644
--- a/docker/Dockerfile
+++ b/docker/Dockerfile
@@ -1,14 +1,18 @@
-FROM debian:8-slim
-
-RUN apt-get update \
-    && apt-get install autoconf libtool nasm libpng-dev automake pkg-config build-essential wget \
-    -yq --no-install-suggests --no-install-recommends --force-yes
-
-WORKDIR /src
-RUN wget --no-check-certificate https://github.com/mozilla/mozjpeg/archive/v3.3.1.tar.gz -O mozjpeg-3.3.1.tar.gz
-RUN tar -xzvf mozjpeg-3.3.1.tar.gz
-WORKDIR /src/mozjpeg-3.3.1
-
-RUN autoreconf -fiv \
-    && ./configure LDFLAGS=-static libpng_LIBS='/usr/lib/x86_64-linux-gnu/libpng12.a -lz' --enable-static --disable-shared \
-    && make -j8
+FROM docker.io/library/alpine:latest
+RUN apk --update --no-cache upgrade && apk add --no-cache \
+    build-base \
+    nasm \
+    cmake \
+    ninja \
+    curl \
+    libpng-dev libpng-static \
+    zlib-dev zlib-static
+RUN adduser -G wheel -D builder
+WORKDIR /home/builder
+USER builder
+ENV mozjpeg_version 4.0.0
+# 2020-11-13 UTC
+ENV SOURCE_DATE_EPOCH 1605225600
+RUN mkdir bin
+COPY /build.sh build.sh
+RUN ["/bin/sh", "build.sh"]
diff --git a/docker/build.sh b/docker/build.sh
new file mode 100644
index 0000000..5520aa0
--- /dev/null
+++ b/docker/build.sh
@@ -0,0 +1,22 @@
+#!/bin/sh
+set -e
+
+curl -fLO "https://github.com/mozilla/mozjpeg/archive/v${mozjpeg_version}.tar.gz"
+tar xf "v${mozjpeg_version}.tar.gz"
+
+export CFLAGS='-pipe -flto -no-pie'
+export LDFLAGS='-flto -no-pie -static -static-libgcc'
+
+# This unsets CMAKE_SHARED_LIBRARY_LINK_C_FLAGS inside CMakeLists.txt,
+# which is necessary to build a static binary. It can't be unset from the CLI.
+sed -E -i.bk '/set\(LIBJPEG_TURBO_V/i\
+set(CMAKE_SHARED_LIBRARY_LINK_C_FLAGS)' "mozjpeg-$mozjpeg_version"/CMakeLists.txt
+
+cmake -S "mozjpeg-$mozjpeg_version" -B build -G Ninja \
+    -D ENABLE_SHARED=OFF \
+    -D CMAKE_INSTALL_PREFIX=/usr/local \
+    -D CMAKE_FIND_LIBRARY_SUFFIXES=.a \
+    -D CMAKE_LINK_SEARCH_END_STATIC=1 -D CMAKE_LINK_SEARCH_START_STATIC=1
+
+cd build && ninja
+strip cjpeg-static
diff --git a/package.json b/package.json
index 6d86413..00880ad 100644
--- a/package.json
+++ b/package.json
@@ -11,7 +11,7 @@
 	"scripts": {
 		"postinstall": "node lib/install.js",
 		"test": "xo && ava --timeout=120s",
-		"build-linux": "docker build --tag imagemin/mozjpeg docker && docker run --rm --volume $(pwd)/vendor/linux:/src/out imagemin/mozjpeg cp cjpeg /src/out"
+		"build-linux": "docker build --tag imagemin/mozjpeg docker/ && docker create --name mozjpeg_ctr imagemin/mozjpeg && docker cp mozjpeg_ctr:/home/builder/build/cjpeg-static ./vendor/linux/cjpeg && docker container rm mozjpeg_ctr"
 	},
 	"files": [
 		"index.js",
diff --git a/vendor/linux/cjpeg b/vendor/linux/cjpeg
index 7477364..bb70e56 100755
Binary files a/vendor/linux/cjpeg and b/vendor/linux/cjpeg differ