diff --git a/kernel/Dockerfile b/kernel/Dockerfile
index a2b9d8375..47175b551 100644
--- a/kernel/Dockerfile
+++ b/kernel/Dockerfile
@@ -20,28 +20,35 @@ RUN if [ $DEBUG -ne "0" ]; then \
 
 # Apply local patches
 COPY patches-${KERNEL_SERIES} /patches
-RUN cd /linux && \
-    set -e && for patch in /patches/*.patch; do \
+WORKDIR /linux
+RUN set -e && for patch in /patches/*.patch; do \
         echo "Applying $patch"; \
         patch -p1 < "$patch"; \
     done
 
-RUN cd /linux && \
-    make defconfig && \
+RUN mkdir /out
+
+# Kernel
+RUN make defconfig && \
     make oldconfig && \
-    make -j "$(getconf _NPROCESSORS_ONLN)" KCFLAGS="-fno-pie"
-RUN cd /linux && \
-    make INSTALL_MOD_PATH=/tmp/kernel-modules modules_install && \
+    make -j "$(getconf _NPROCESSORS_ONLN)" KCFLAGS="-fno-pie" && \
+    cp arch/x86_64/boot/bzImage /out/kernel && \
+    cp System.map /out
+
+# Modules
+RUN make INSTALL_MOD_PATH=/tmp/kernel-modules modules_install && \
     ( DVER=$(basename $(find /tmp/kernel-modules/lib/modules/ -mindepth 1 -maxdepth 1)) && \
       cd /tmp/kernel-modules/lib/modules/$DVER && \
       rm build source && \
       ln -s /usr/src/linux-headers-$DVER build ) && \
-    mkdir -p /tmp/kernel-headers/usr && \
-    make INSTALL_HDR_PATH=/tmp/kernel-headers/usr headers_install && \
-    ( cd /tmp/kernel-headers && tar cf /kernel-headers.tar usr ) && \
-    ( cd /tmp/kernel-modules && tar cf /kernel-modules.tar lib ) && \
-    cp vmlinux arch/x86_64/boot/bzImage /
+    ( cd /tmp/kernel-modules && tar cf /out/kernel.tar lib )
 
+# Headers (userspace API)
+RUN mkdir -p /tmp/kernel-headers/usr && \
+    make INSTALL_HDR_PATH=/tmp/kernel-headers/usr headers_install && \
+    ( cd /tmp/kernel-headers && tar cf /out/kernel-headers.tar usr )
+
+# Headers (kernel development)
 RUN DVER=$(basename $(find /tmp/kernel-modules/lib/modules/ -mindepth 1 -maxdepth 1)) && \
     dir=/tmp/usr/src/linux-headers-$DVER && \
     mkdir -p $dir && \
@@ -49,17 +56,13 @@ RUN DVER=$(basename $(find /tmp/kernel-modules/lib/modules/ -mindepth 1 -maxdept
     cd /linux && \
     cp -a include "$dir" && \
     mkdir -p "$dir"/arch/x86 && cp -a arch/x86/include "$dir"/arch/x86/ && \
-    ( cd /tmp && tar cf /kernel-dev.tar usr/src )
+    ( cd /tmp && tar cf /out/kernel-dev.tar usr/src )
 
-RUN printf "KERNEL_SOURCE=${KERNEL_SOURCE}\n" > /kernel-source-info
+RUN printf "KERNEL_SOURCE=${KERNEL_SOURCE}\n" > /out/kernel-source-info
 
 
 FROM linuxkit/toybox-media:eee3dd4d72cd784801e95b1781e6c4f9d8a5e5eb@sha256:7f940e687164ee2676e11c61705c79f7dd2d144ee87ad17a494848a7045f5f53
 ENTRYPOINT []
 CMD []
 WORKDIR /
-COPY --from=kernel-build bzImage /kernel
-COPY --from=kernel-build kernel-headers.tar /
-COPY --from=kernel-build kernel-modules.tar /kernel.tar
-COPY --from=kernel-build kernel-dev.tar /
-COPY --from=kernel-build kernel-source-info /
+COPY --from=kernel-build /out/* /