diff --git a/.gitlab-ci/Dockerfile b/.gitlab-ci/fedora-gtk3.Dockerfile
similarity index 100%
rename from .gitlab-ci/Dockerfile
rename to .gitlab-ci/fedora-gtk3.Dockerfile
diff --git a/.gitlab-ci/run-docker.sh b/.gitlab-ci/run-docker.sh
index 789284130f..ef0f56154e 100755
--- a/.gitlab-ci/run-docker.sh
+++ b/.gitlab-ci/run-docker.sh
@@ -1,19 +1,135 @@
 #!/bin/bash
-#
-# This script builds an image from the Dockerfile, starts a container with
-# the parent directory mounted as working directory and start a bash session
-# there so you can test things.
-# Once you are happy you can push it to the docker hub:
-#     sudo docker push "${TAG}"
+
+read_arg() {
+    # $1 = arg name
+    # $2 = arg value
+    # $3 = arg parameter
+    local rematch='^[^=]*=(.*)$'
+    if [[ $2 =~ $rematch ]]; then
+        read "$1" <<< "${BASH_REMATCH[1]}"
+    else
+        read "$1" <<< "$3"
+        # There is no way to shift our callers args, so
+        # return 1 to indicate they should do it instead.
+        return 1
+    fi
+}
 
 set -e
 
-TAG="registry.gitlab.gnome.org/gnome/gtk/gtk-3-24:v2"
+build=0
+run=0
+push=0
+list=0
+print_help=0
+no_login=0
 
-# HOST_USER_ID gets used to create a user with the same ID so that files
-# created in the mounted volume have the same owner
-sudo docker build \
-    --build-arg HOST_USER_ID="$UID" --tag "${TAG}" --file "Dockerfile" .
-sudo docker run --security-opt label=disable \
-    --rm --volume "$(pwd)/..:/home/user/app" --workdir "/home/user/app" \
-    --tty --interactive "${TAG}" bash
+while (($# > 0)); do
+        case "${1%%=*}" in
+                build) build=1;;
+                run) run=1;;
+                push) push=1;;
+                list) list=1;;
+                help) print_help=1;;
+                --base|-b) read_arg base "$@" || shift;;
+                --base-version) read_arg base_version "$@" || shift;;
+                --no-login) no_login=1;;
+                *) echo -e "\e[1;31mERROR\e[0m: Unknown option '$1'"; exit 1;;
+        esac
+        shift
+done
+
+if [ $print_help == 1 ]; then
+        echo "$0 - Build and run Docker images"
+        echo ""
+        echo "Usage: $0 <command> [options] [basename]"
+        echo ""
+        echo "Available commands"
+        echo ""
+        echo "  build --base=<BASENAME> - Build Docker image <BASENAME>.Dockerfile"
+        echo "  run --base=<BASENAME>   - Run Docker image <BASENAME>"
+        echo "  push --base=<BASENAME>  - Push Docker image <BASENAME> to the registry"
+        echo "  list                    - List available images"
+        echo "  help                    - This help message"
+        echo ""
+        exit 0
+fi
+
+cd "$(dirname "$0")"
+
+if [ $list == 1 ]; then
+        echo "Available Docker images:"
+        for f in *.Dockerfile; do
+                filename=$( basename -- "$f" )
+                basename="${filename%.*}"
+
+                echo -e "  \e[1;39m$basename\e[0m"
+        done
+        exit 0
+fi
+
+# All commands after this require --base to be set
+if [ -z $base ]; then
+        echo "Usage: $0 <command>"
+        exit 1
+fi
+
+if [ ! -f "$base.Dockerfile" ]; then
+        echo -e "\e[1;31mERROR\e[0m: Dockerfile for '$base' not found"
+        exit 1
+fi
+
+if [ -z $base_version ]; then
+        base_version="latest"
+else
+        base_version="v$base_version"
+fi
+
+if [ ! -x "$(command -v docker)" ] || [ docker --help |& grep -q podman ]; then
+        # Docker is actually implemented by podman, and its OCI output
+        # is incompatible with some of the dockerd instances on GitLab
+        # CI runners.
+        echo "Using: Podman"
+        format="--format docker"
+        CMD="podman"
+else
+        echo "Using: Docker"
+        format=""
+        CMD="sudo socker"
+fi
+
+REGISTRY="registry.gitlab.gnome.org"
+TAG="${REGISTRY}/gnome/gtk/${base}:${base_version}"
+
+if [ $build == 1 ]; then
+        echo -e "\e[1;32mBUILDING\e[0m: ${base} as ${TAG}"
+        ${CMD} build \
+                ${format} \
+                --build-arg HOST_USER_ID="$UID" \
+                --tag "${TAG}" \
+                --file "${base}.Dockerfile" .
+        exit $?
+fi
+
+if [ $push == 1 ]; then
+        echo -e "\e[1;32mPUSHING\e[0m: ${base} as ${TAG}"
+
+        if [ $no_login == 0 ]; then
+                ${CMD} login ${REGISTRY}
+        fi
+
+        ${CMD} push ${TAG}
+        exit $?
+fi
+
+if [ $run == 1 ]; then
+        echo -e "\e[1;32mRUNNING\e[0m: ${base} as ${TAG}"
+        ${CMD} run \
+                --rm \
+                --volume "$(pwd)/..:/home/user/app" \
+                --workdir "/home/user/app" \
+                --tty \
+                --interactive "${TAG}" \
+                bash
+        exit $?
+fi