diff --git a/Dockerfile b/Dockerfile
index e504e94..673e336 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -16,14 +16,37 @@ WORKDIR /build
 ARG CORES=4
 
 ENV TOOLCHAIN_PREFIX=/opt/llvm-mingw
+
+# Build and strip the LLVM installation
+COPY build-llvm.sh strip-llvm.sh ./
+RUN ./build-llvm.sh $TOOLCHAIN_PREFIX && \
+    ./strip-llvm.sh $TOOLCHAIN_PREFIX && \
+    rm -rf /build
+
 ENV TOOLCHAIN_ARCHS="i686 x86_64 armv7 aarch64"
 
-# Build everything and clean up, in one step
-COPY *.sh libssp-Makefile ./
+# Install the usual $TUPLE-clang binaries
 COPY wrappers/*.sh ./wrappers/
 COPY wrappers/*.c ./wrappers/
-RUN ./build-all.sh $TOOLCHAIN_PREFIX && \
-    ./strip-llvm.sh $TOOLCHAIN_PREFIX && \
+COPY install-wrappers.sh .
+RUN ./install-wrappers.sh $TOOLCHAIN_PREFIX && \
+    rm -rf /build
+
+# Build MinGW-w64, compiler-rt and mingw-w64's extra libraries
+COPY build-mingw-w64.sh build-compiler-rt.sh build-mingw-w64-libraries.sh ./
+RUN ./build-mingw-w64.sh $TOOLCHAIN_PREFIX && \
+    ./build-compiler-rt.sh $TOOLCHAIN_PREFIX && \
+    ./build-mingw-w64-libraries.sh $TOOLCHAIN_PREFIX && \
+    rm -rf /build
+
+# Build libunwind/libcxxabi/libcxx
+COPY build-libcxx.sh merge-archives.sh ./
+RUN ./build-libcxx.sh $TOOLCHAIN_PREFIX && \
+    rm -rf /build
+
+# Build libssp
+COPY build-libssp.sh libssp-Makefile ./
+RUN ./build-libssp.sh $TOOLCHAIN_PREFIX && \
     rm -rf /build
 
 # Cheating: Pull strip and objcopy from the normal binutils package.