diff --git a/.travis.yml b/.travis.yml
index 4720717..70b0178 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -8,6 +8,7 @@ env:
     - CC=gcc ARCH_SUFFIX=amd64 ARCH_NATIVE=1 MINIMAL=
     - CC=arm-linux-gnueabihf-gcc ARCH_SUFFIX=armhf ARCH_NATIVE= MINIMAL=
     - CC=aarch64-linux-gnu-gcc ARCH_SUFFIX=arm64 ARCH_NATIVE= MINIMAL=
+    - CFLAGS="-m32" ARCH_SUFFIX=i386 ARCH_NATIVE= MINIMAL=
     - CC=gcc ARCH_SUFFIX=amd64 ARCH_NATIVE=1 MINIMAL=1
   global:
     - SIGN_BINARIES=1
diff --git a/Dockerfile b/Dockerfile
index 48ae4a5..a71d0d6 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -1,5 +1,7 @@
 FROM ubuntu:trusty
 
+ARG ARCH_SUFFIX
+
 COPY ci/install_deps.sh /install_deps.sh
 RUN /install_deps.sh
 
diff --git a/ci/install_deps.sh b/ci/install_deps.sh
index ce5d104..b83637d 100755
--- a/ci/install_deps.sh
+++ b/ci/install_deps.sh
@@ -1,14 +1,27 @@
 #!/bin/bash
 set -o errexit
 set -o nounset
+set -o xtrace
 
-apt-get update
-
-apt-get install --no-install-recommends --yes \
+DEPS=(
   build-essential git gdb valgrind cmake rpm \
   python-dev libcap-dev python-pip python-virtualenv \
-  hardening-includes gnupg \
-  gcc-aarch64-linux-gnu binutils-aarch64-linux-gnu libc6-dev-arm64-cross \
-  gcc-arm-linux-gnueabihf binutils-arm-linux-gnueabi libc6-dev-armhf-cross
+  hardening-includes gnupg
+)
 
+if [[ "$ARCH_SUFFIX" = "amd64" ]]; then
+  true
+elif [[ "$ARCH_SUFFIX" = "armhf" ]]; then
+  DEPS+=(gcc-arm-linux-gnueabihf binutils-arm-linux-gnueabi libc6-dev-armhf-cross)
+elif [[ "$ARCH_SUFFIX" = "arm64" ]]; then
+  DEPS+=(gcc-aarch64-linux-gnu binutils-aarch64-linux-gnu libc6-dev-arm64-cross)
+elif [[ "$ARCH_SUFFIX" = "i386" ]]; then
+  DEPS+=(libc6-dev-i386  gcc-multilib)
+else
+  echo "Unknown ARCH_SUFFIX=${ARCH_SUFFIX}"
+  exit 1
+fi
+
+apt-get update
+apt-get install --no-install-recommends --yes "${DEPS[@]}"
 rm -rf /var/lib/apt/lists/*
diff --git a/ci/run_build.sh b/ci/run_build.sh
index 7658ac7..6eaa35b 100755
--- a/ci/run_build.sh
+++ b/ci/run_build.sh
@@ -7,7 +7,6 @@ set -o pipefail
 # Default compiler
 : ${CC:="gcc"}
 
-echo "CC=${CC}"
 
 # Paths
 : ${SOURCE_DIR:="."}
@@ -30,12 +29,17 @@ export FORCE_SUBREAPER
 
 # Our build platform doesn't have those newer Linux flags, but we want Tini to have subreaper support
 # We also use those in our tests
-CFLAGS="-DPR_SET_CHILD_SUBREAPER=36 -DPR_GET_CHILD_SUBREAPER=37"
+CFLAGS="${CFLAGS-} -DPR_SET_CHILD_SUBREAPER=36 -DPR_GET_CHILD_SUBREAPER=37"
 if [[ "${FORCE_SUBREAPER}" -eq 1 ]]; then
   # If FORCE_SUBREAPER is requested, then we set those CFLAGS for the Tini build
   export CFLAGS
 fi
 
+echo "CC=${CC}"
+echo "CFLAGS=${CFLAGS}"
+echo "ARCH_SUFFIX=${ARCH_SUFFIX-}"
+echo "ARCH_NATIVE=${ARCH_NATIVE-}"
+
 # Ensure Python output is not buffered (to make tests output clearer)
 export PYTHONUNBUFFERED=1
 
@@ -53,7 +57,7 @@ cmake "${CMAKE_ARGS[@]}"
 pushd "${BUILD_DIR}"
 make clean
 make
-if [[ -n "${ARCH_NATIVE:=}" ]]; then
+if [[ -n "${ARCH_NATIVE-}" ]]; then
   make package
 fi
 popd
@@ -61,8 +65,8 @@ popd
 pkg_version="$(cat "${BUILD_DIR}/VERSION")"
 
 
-if [[ -n "${ARCH_NATIVE:=}" ]]; then
-  echo "Built native package (ARCH_NATIVE=${ARCH_NATIVE})"
+if [[ -n "${ARCH_NATIVE-}" ]]; then
+  echo "Built native package (ARCH_NATIVE=${ARCH_NATIVE-})"
   echo "Running smoke and internal tests"
 
   BIN_TEST_DIR="${BUILD_DIR}/bin-test"
@@ -194,7 +198,7 @@ if [[ -n "${ARCH_NATIVE:=}" ]]; then
   # Run tests
   python "${SOURCE_DIR}/test/run_inner_tests.py"
 else
-  if [[ ! -n "${ARCH_SUFFIX:=}" ]]; then
+  if [[ ! -n "${ARCH_SUFFIX-}" ]]; then
     echo "Built cross package, but $ARCH_SUFFIX is empty!"
     exit 1
   fi
@@ -210,30 +214,30 @@ mkdir -p "${DIST_DIR}"
 TINIS=()
 
 for tini in tini tini-static; do
-  if [[ -n "${ARCH_SUFFIX:=}" ]]; then
+  if [[ -n "${ARCH_SUFFIX-}" ]]; then
     to="${DIST_DIR}/${tini}-${ARCH_SUFFIX}"
     TINIS+=("$to")
     cp "${BUILD_DIR}/${tini}" "$to"
   fi
 
-  if [[ -n "${ARCH_NATIVE:=}" ]]; then
+  if [[ -n "${ARCH_NATIVE-}" ]]; then
     to="${DIST_DIR}/${tini}"
     TINIS+=("$to")
     cp "${BUILD_DIR}/${tini}" "$to"
   fi
 done
 
-if [[ -n "${ARCH_NATIVE:=}" ]]; then
+if [[ -n "${ARCH_NATIVE-}" ]]; then
   for pkg_format in deb rpm; do
     src="${BUILD_DIR}/tini_${pkg_version}.${pkg_format}"
 
-    if [[ -n "${ARCH_SUFFIX:=}" ]]; then
+    if [[ -n "${ARCH_SUFFIX-}" ]]; then
       to="${DIST_DIR}/tini_${pkg_version}-${ARCH_SUFFIX}.${pkg_format}"
       TINIS+=("$to")
       cp "$src" "$to"
     fi
 
-    if [[ -n "${ARCH_NATIVE:=}" ]]; then
+    if [[ -n "${ARCH_NATIVE-}" ]]; then
       to="${DIST_DIR}/tini_${pkg_version}.${pkg_format}"
       TINIS+=("$to")
       cp "$src" "$to"
diff --git a/ddist.sh b/ddist.sh
index 9370912..8d576b0 100755
--- a/ddist.sh
+++ b/ddist.sh
@@ -2,17 +2,23 @@
 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"
+IMG="tini-build-${suffix}"
 SRC="/tini"
 
 # Cleanup the build dir
 rm -f "${HERE}/dist"/*
 
 # Create the build image
-docker build -t "${IMG}" .
+docker build --build-arg "ARCH_SUFFIX=${suffix}" -t "${IMG}" .
 
 # Run test without subreaper support, don't copy build files here
 docker run -it --rm \
@@ -22,7 +28,8 @@ docker run -it --rm \
   -e FORCE_SUBREAPER="${FORCE_SUBREAPER:="1"}" \
   -e GPG_PASSPHRASE="${GPG_PASSPHRASE:=}" \
   -e CC="${CC:=gcc}" \
+  -e CFLAGS="${CFLAGS-}" \
   -e ARCH_NATIVE="${ARCH_NATIVE-1}" \
-  -e ARCH_SUFFIX="${ARCH_SUFFIX-}" \
+  -e ARCH_SUFFIX="${suffix}" \
   -e MINIMAL="${MINIMAL-}" \
   "${IMG}" "${SRC}/ci/run_build.sh"
diff --git a/dtest.sh b/dtest.sh
index 00e0894..fa0f4aa 100755
--- a/dtest.sh
+++ b/dtest.sh
@@ -4,6 +4,11 @@ set -o nounset
 
 IMG="tini"
 
+if [[ "$#" != 1 ]]; then
+  echo "Usage: $0 ARCH_SUFFIX"
+  exit 1
+fi
+suffix="$1"
 
-docker build -t "${IMG}" .
-python test/run_outer_tests.py  "${IMG}"
+IMG="tini-build-${suffix}"
+python test/run_outer_tests.py "${IMG}"