diff --git a/Dockerfile b/Dockerfile
index eea5dbd..c161f09 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -63,3 +63,8 @@ RUN cd test && \
             $arch-w64-mingw32-clang++ $test.cpp -o $test-$arch.exe || exit 1; \
         done; \
     done
+
+# Strip the final toolchain. (This doesn't reduce the total docker image
+# size as long as it is in a separate RUN layer though.)
+COPY strip-llvm.sh .
+RUN ./strip-llvm.sh $TOOLCHAIN_PREFIX
diff --git a/strip-llvm.sh b/strip-llvm.sh
new file mode 100755
index 0000000..870f295
--- /dev/null
+++ b/strip-llvm.sh
@@ -0,0 +1,35 @@
+#!/bin/sh
+
+set -e
+
+if [ $# -lt 1 ]; then
+    echo $0 dir
+    exit 1
+fi
+PREFIX="$1"
+cd "$PREFIX"
+
+cd bin
+for i in bugpoint c-index-test clang-* dsymutil git-clang-format llc lli llvm-* obj2yaml opt sancov sanstats scan-build scan-view verify-uselistorder yaml2obj; do
+    case $i in
+    *.sh)
+        ;;
+    clang++|clang-*.*|clang-cpp)
+        ;;
+    llvm-ar|llvm-cvtres|llvm-dlltool|llvm-nm|llvm-objdump|llvm-ranlib|llvm-rc|llvm-readobj|llvm-strings)
+        ;;
+    *)
+        if [ -f $i ]; then
+            rm $i
+        fi
+        ;;
+    esac
+done
+cd ..
+rm -rf share libexec
+cd include
+rm -rf clang clang-c lld llvm llvm-c
+cd ..
+cd lib
+rm -rf lib*.a *.so* *.dylib* cmake
+cd ..