diff --git a/.travis.yml b/.travis.yml
index fc5730b085..069aeeff3c 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -32,7 +32,7 @@ matrix:
       services:
         - docker
       before_install:
-      script: ci/run-linux32-docker.sh
+      script: ci/run-docker.sh
     - env: jobname=StaticAnalysis
       os: linux
       compiler:
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index 675c3a43c9..11413f66f8 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -489,14 +489,14 @@ jobs:
        test "$GITFILESHAREPWD" = '$(gitfileshare.pwd)' || ci/mount-fileshare.sh //gitfileshare.file.core.windows.net/test-cache gitfileshare "$GITFILESHAREPWD" "$HOME/test-cache" || exit 1
 
        res=0
-       sudo AGENT_OS="$AGENT_OS" BUILD_BUILDNUMBER="$BUILD_BUILDNUMBER" BUILD_REPOSITORY_URI="$BUILD_REPOSITORY_URI" BUILD_SOURCEBRANCH="$BUILD_SOURCEBRANCH" BUILD_SOURCEVERSION="$BUILD_SOURCEVERSION" SYSTEM_PHASENAME="$SYSTEM_PHASENAME" SYSTEM_TASKDEFINITIONSURI="$SYSTEM_TASKDEFINITIONSURI" SYSTEM_TEAMPROJECT="$SYSTEM_TEAMPROJECT" CC=$CC MAKEFLAGS="$MAKEFLAGS" bash -lxc ci/run-linux32-docker.sh || res=1
+       sudo AGENT_OS="$AGENT_OS" BUILD_BUILDNUMBER="$BUILD_BUILDNUMBER" BUILD_REPOSITORY_URI="$BUILD_REPOSITORY_URI" BUILD_SOURCEBRANCH="$BUILD_SOURCEBRANCH" BUILD_SOURCEVERSION="$BUILD_SOURCEVERSION" SYSTEM_PHASENAME="$SYSTEM_PHASENAME" SYSTEM_TASKDEFINITIONSURI="$SYSTEM_TASKDEFINITIONSURI" SYSTEM_TEAMPROJECT="$SYSTEM_TEAMPROJECT" CC=$CC MAKEFLAGS="$MAKEFLAGS" jobname=Linux32 bash -lxc ci/run-docker.sh || res=1
 
        sudo chmod a+r t/out/TEST-*.xml
        test ! -d t/failed-test-artifacts || sudo chmod a+r t/failed-test-artifacts
 
        test "$GITFILESHAREPWD" = '$(gitfileshare.pwd)' || sudo umount "$HOME/test-cache" || res=1
        exit $res
-    displayName: 'ci/run-linux32-docker.sh'
+    displayName: 'jobname=Linux32 ci/run-docker.sh'
     env:
       GITFILESHAREPWD: $(gitfileshare.pwd)
   - task: PublishTestResults@2
diff --git a/ci/run-linux32-build.sh b/ci/run-docker-build.sh
similarity index 93%
rename from ci/run-linux32-build.sh
rename to ci/run-docker-build.sh
index 44bb332f64..a05b48c559 100755
--- a/ci/run-linux32-build.sh
+++ b/ci/run-docker-build.sh
@@ -1,16 +1,16 @@
 #!/bin/sh
 #
-# Build and test Git in a 32-bit environment
+# Build and test Git inside container
 #
 # Usage:
-#   run-linux32-build.sh <host-user-id>
+#   run-docker-build.sh <host-user-id>
 #
 
 set -ex
 
 if test $# -ne 1 || test -z "$1"
 then
-	echo >&2 "usage: run-linux32-build.sh <host-user-id>"
+	echo >&2 "usage: run-docker-build.sh <host-user-id>"
 	exit 1
 fi
 
diff --git a/ci/run-linux32-docker.sh b/ci/run-docker.sh
similarity index 53%
rename from ci/run-linux32-docker.sh
rename to ci/run-docker.sh
index 54186b6aa7..3881f99b53 100755
--- a/ci/run-linux32-docker.sh
+++ b/ci/run-docker.sh
@@ -1,16 +1,26 @@
 #!/bin/sh
 #
-# Download and run Docker image to build and test 32-bit Git
+# Download and run Docker image to build and test Git
 #
 
 . ${0%/*}/lib.sh
 
-docker pull daald/ubuntu32:xenial
+case "$jobname" in
+Linux32)
+	CI_CONTAINER="daald/ubuntu32:xenial"
+	;;
+*)
+	exit 1
+	;;
+esac
+
+docker pull "$CI_CONTAINER"
 
 # Use the following command to debug the docker build locally:
-# $ docker run -itv "${PWD}:/usr/src/git" --entrypoint /bin/bash daald/ubuntu32:xenial
+# <host-user-id> must be 0 if podman is used as drop-in replacement for docker
+# $ docker run -itv "${PWD}:/usr/src/git" --entrypoint /bin/sh "$CI_CONTAINER"
 # root@container:/# export jobname=<jobname>
-# root@container:/# /usr/src/git/ci/run-linux32-build.sh <host-user-id>
+# root@container:/# /usr/src/git/ci/run-docker-build.sh <host-user-id>
 
 container_cache_dir=/tmp/travis-cache
 
@@ -26,8 +36,8 @@ docker run \
 	--env cache_dir="$container_cache_dir" \
 	--volume "${PWD}:/usr/src/git" \
 	--volume "$cache_dir:$container_cache_dir" \
-	daald/ubuntu32:xenial \
-	/usr/src/git/ci/run-linux32-build.sh $(id -u $USER)
+	"$CI_CONTAINER" \
+	/usr/src/git/ci/run-docker-build.sh $(id -u $USER)
 
 check_unignored_build_artifacts