diff --git a/Dockerfile b/Dockerfile
index 4ee1a8b..8d77935 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -7,3 +7,12 @@ RUN /install_deps.sh
 
 # Pre-install those here for faster local builds.
 RUN CFLAGS="-DPR_SET_CHILD_SUBREAPER=36 -DPR_GET_CHILD_SUBREAPER=37" pip install psutil python-prctl bitmap
+
+ARG ARCH_NATIVE
+ARG CC
+
+# Persist ARGs into the image
+
+ENV ARCH_SUFFIX="$ARCH_SUFFIX" \
+    ARCH_NATIVE="$ARCH_NATIVE" \
+    CC="$CC"
diff --git a/ddist.sh b/ddist.sh
index 0625399..eed7d46 100755
--- a/ddist.sh
+++ b/ddist.sh
@@ -2,35 +2,46 @@
 set -o errexit
 set -o nounset
 
-if [[ "$#" != 1 ]]; then
-  echo "Usage: $0 ARCH_SUFFIX"
-  exit 1
-fi
-suffix="$1"
-
 REL_HERE=$(dirname "${BASH_SOURCE}")
 HERE=$(cd "${REL_HERE}"; pwd)
 
-IMG="tini-build-${suffix}"
-SRC="/tini"
+IMG="tini-build"
+
+if [[ -n "${ARCH_SUFFIX-}" ]]; then
+  IMG="${IMG}_${ARCH_SUFFIX}"
+fi
+
+if [[ -n "${ARCH_NATIVE-}" ]]; then
+  IMG="${IMG}_native"
+fi
+
+if [[ -n "${CC-}" ]]; then
+  IMG="${IMG}_${CC}"
+fi
 
 # Cleanup the build dir
 rm -f "${HERE}/dist"/*
 
 # Create the build image
-docker build --build-arg "ARCH_SUFFIX=${suffix}" -t "${IMG}" .
+echo "build: ${IMG}"
+
+docker build \
+  --build-arg "ARCH_SUFFIX=${ARCH_SUFFIX-}" \
+  --build-arg "ARCH_NATIVE=${ARCH_NATIVE-}" \
+  --build-arg "CC=${CC-gcc}" \
+  -t "${IMG}" \
+  .
+
+# Build new Tini
+SRC="/tini"
 
-# Run test without subreaper support, don't copy build files here
 docker run -it --rm \
   --volume="${HERE}:${SRC}" \
   -e BUILD_DIR=/tmp/tini-build \
   -e SOURCE_DIR="${SRC}" \
-  -e FORCE_SUBREAPER="${FORCE_SUBREAPER:="1"}" \
-  -e GPG_PASSPHRASE="${GPG_PASSPHRASE:=}" \
-  -e CC="${CC:=gcc}" \
+  -e FORCE_SUBREAPER="${FORCE_SUBREAPER-1}" \
+  -e GPG_PASSPHRASE="${GPG_PASSPHRASE-}" \
   -e CFLAGS="${CFLAGS-}" \
-  -e ARCH_NATIVE="${ARCH_NATIVE-}" \
-  -e ARCH_SUFFIX="${suffix}" \
   -e MINIMAL="${MINIMAL-}" \
   -u "$(id -u):$(id -g)" \
   "${IMG}" "${SRC}/ci/run_build.sh"