diff --git a/.github/workflows/release.yml b/.github/workflows/release.yml
index dd95dcba0175..2c51d7d6562c 100644
--- a/.github/workflows/release.yml
+++ b/.github/workflows/release.yml
@@ -52,7 +52,7 @@ jobs:
     permissions: {}
     runs-on: ubuntu-latest
     container:
-      image: ghcr.io/cockpit-project/unit-tests
+      image: quay.io/cockpit/tasks:latest
       options: --user root
     steps:
       - name: Checkout website repository
diff --git a/.github/workflows/unit-tests-refresh.yml b/.github/workflows/unit-tests-refresh.yml
deleted file mode 100644
index d3b88ebd1d29..000000000000
--- a/.github/workflows/unit-tests-refresh.yml
+++ /dev/null
@@ -1,48 +0,0 @@
-name: unit-test-refresh
-on:
-  schedule:
-    # auto-refresh every Sunday evening
-    - cron: '0 22 * * 0'
-  # can be run manually on https://github.com/cockpit-project/cockpit/actions
-  workflow_dispatch:
-jobs:
-  # we do both builds and all tests in a single run, so that we only upload the containers on success
-  refresh:
-    runs-on: ubuntu-22.04
-    permissions:
-      contents: read
-      packages: write
-    timeout-minutes: 60
-    steps:
-      - name: Clone repository
-        uses: actions/checkout@v4
-        with:
-          # need this to also fetch tags
-          fetch-depth: 0
-
-      - name: Build fresh containers
-        timeout-minutes: 10
-        run: containers/unit-tests/build
-
-      - name: Run amd64 gcc check-memory test
-        timeout-minutes: 20
-        run: containers/unit-tests/start --verbose --env=CC=gcc --image-tag=latest --make check-memory
-
-      - name: Run amd64 clang distcheck test
-        timeout-minutes: 15
-        run: containers/unit-tests/start --verbose --env=CC=clang --image-tag=latest --make distcheck
-
-      - name: Run amd64 gcc check test
-        timeout-minutes: 15
-        run: containers/unit-tests/start --verbose --env=CC=gcc --image-tag=latest --make check
-
-      - name: Run pytest-cov test
-        timeout-minutes: 15
-        run: containers/unit-tests/start --verbose --env=CC=gcc --image-tag=latest --make pytest-cov
-
-      - name: Log into container registry
-        run: podman login -u ${{ github.actor }} -p ${{ secrets.GITHUB_TOKEN }} ghcr.io
-
-      - name: Push containers to registry
-        run: |
-          podman push ghcr.io/cockpit-project/unit-tests:latest
diff --git a/.github/workflows/unit-tests.yml b/.github/workflows/unit-tests.yml
index 6450def79b95..470159c908ab 100644
--- a/.github/workflows/unit-tests.yml
+++ b/.github/workflows/unit-tests.yml
@@ -4,37 +4,33 @@ jobs:
   unit-tests:
     runs-on: ubuntu-22.04
     permissions: {}
+    container:
+      image: quay.io/cockpit/tasks:latest
+      options: --user 1001
     strategy:
       matrix:
-        startarg:
-          - { make: 'check-memory', tag: 'latest' }
-          - { make: 'distcheck', tag: 'latest' }
+        target:
+          - check-memory
+          - distcheck
           # this runs static code checks, unlike distcheck
-          - { make: 'check', tag: 'latest' }
-          - { make: 'pytest-cov', tag: 'latest' }
+          - check
+          - pytest-cov
       fail-fast: false
     timeout-minutes: 60
+    env:
+      FORCE_COLOR: 1
+      TEST_BROWSER: firefox
+      CFLAGS: '-O2'
     steps:
       - name: Clone repository
         uses: actions/checkout@v4
         with:
           # need this to also fetch tags
           fetch-depth: 0
+          submodules: true
 
-      - name: Build unit test container if it changed
-        run: |
-          changes=$(git diff --name-only origin/${{ github.event.pull_request.base.ref }}..HEAD -- containers/unit-tests/)
-          if [ -n "${changes}" ]; then
-            containers/unit-tests/build
-          fi
-
-      - name: Run unit-tests container
+      - name: Run unit test
         timeout-minutes: 30
         run: |
-          containers/unit-tests/start \
-              --verbose \
-              --env=FORCE_COLOR=1 \
-              --env=CFLAGS='-O2' \
-              --env=EXTRA_DISTCHECK_CONFIGURE_FLAGS='${{ matrix.startarg.distcheck_flags }}' \
-              --image-tag='${{ matrix.startarg.tag }}' \
-              --make '${{ matrix.startarg.make }}'
+            ./autogen.sh
+            make -j$(nproc) '${{ matrix.target }}'
diff --git a/containers/unit-tests/Dockerfile b/containers/unit-tests/Dockerfile
deleted file mode 100644
index 19d8200b8a8c..000000000000
--- a/containers/unit-tests/Dockerfile
+++ /dev/null
@@ -1,26 +0,0 @@
-ARG debian_arch=amd64
-FROM docker.io/${debian_arch}/debian:testing
-
-ARG personality=linux64
-ENV personality=${personality}
-
-COPY setup.sh /
-RUN ${personality} /setup.sh ${personality} && rm -rf /setup.sh
-
-# 'builder' user created in setup.sh
-USER builder
-WORKDIR /home/builder
-
-ENV LANG=C.UTF-8
-
-# HACK: unbreak distcheck on Debian: https://bugs.debian.org/1035546
-ENV DEB_PYTHON_INSTALL_LAYOUT=deb
-
-VOLUME /source
-
-COPY entrypoint /
-ENTRYPOINT ["/entrypoint"]
-CMD ["/bin/bash"]
-
-# for filtering from our 'exec' script
-LABEL org.cockpit-project.container=unit-tests
diff --git a/containers/unit-tests/README.md b/containers/unit-tests/README.md
deleted file mode 100644
index d257d8acffc9..000000000000
--- a/containers/unit-tests/README.md
+++ /dev/null
@@ -1,71 +0,0 @@
-# Cockpit unit test container
-
-This container has all build dependencies and toolchains (GCC and clang) that we
-want to exercise Cockpit with, mostly for `make distcheck` and `make check-memory`.
-This container runs on [GitHub](.github/workflows/unit-tests.yml), but can be easily
-run locally too.
-
-It assumes that the Cockpit source git checkout is available in `/source`. It
-will not modify that directory or take uncommitted changes into account, but it
-will re-use an already existing `node_modules/` directory.
-
-The scripts can use either podman (preferred) or docker. If you use docker, you
-need to run all commands as root. With podman the containers work as either user
-or root.
-
-## Building
-
-The `build` script will build the `cockpit/unit-tests` container.
-
-## Running tests
-
-You need to disable SELinux with `sudo setenforce 0` for this. There is no
-other way for the container to access the files in your build tree (do *not*
-use the `--volume` `:Z` option, as that will destroy the file labels on the
-host).
-
-Tests in that container get started with the `start` script.  By default, this
-script runs the unit tests on amd64.  The script accepts a number of arguments
-to modify its behaviour:
-
- - `--env CC=othercc` to set the `CC` environment variable inside the container (ie:
-   to build with a different compiler)
- - `--image-tag` to specify a different tag to use for the `cockpit/unit-tests` image
-
-Additionally, a testing scenario can be provided with specifying a `make` target.
-Supported scenarios are:
-
- - `check-memory`: runs 'make check-memory' (ie: run the unit tests under valgrind)
- - `distcheck`: runs 'make distcheck' and some related checks
- - `pycheck`: runs browser unit tests against the Python bridge
-
-Some examples:
-
-    $ ./start --make check-memory                 # run the valgrind tests on amd64
-
-    $ ./start --env=CC=clang --make check-memory  # run the valgrind tests, compiled with clang
-
-## Debugging tests
-
-For interactive debugging, run a shell in the container:
-
-    $ ./start
-
-You will find the cockpit source tree (from the host) mounted at `/source` in
-the container. Run
-
-    $ /source/autogen.sh
-
-to create a build tree, then you can run any make or other debugging command
-interactively.
-
-You can also attach to another container using the provided `exec` script.  For example:
-
-    $ ./exec uname -a   # run a command as the "builder" user
-
-    $ ./exec --root     # start a shell as root
-
-## More Info
-
- * [Cockpit Project](https://cockpit-project.org)
- * [Cockpit Development](https://github.com/cockpit-project/cockpit)
diff --git a/containers/unit-tests/build b/containers/unit-tests/build
deleted file mode 100755
index b100a1f7a706..000000000000
--- a/containers/unit-tests/build
+++ /dev/null
@@ -1,6 +0,0 @@
-#!/bin/sh
-set -eu
-
-dir=$(dirname "$0")
-
-podman build --build-arg debian_arch=amd64 --build-arg personality=linux64 -t ghcr.io/cockpit-project/unit-tests ${dir}
diff --git a/containers/unit-tests/entrypoint b/containers/unit-tests/entrypoint
deleted file mode 100755
index 8a53d1074499..000000000000
--- a/containers/unit-tests/entrypoint
+++ /dev/null
@@ -1,12 +0,0 @@
-#!/bin/sh -e
-
-export TEST_BROWSER=firefox
-
-printf "Host: " && uname -srvm
-
-. /usr/lib/os-release
-printf "Container: \${NAME} \${VERSION} / " && ${personality} uname -nrvm
-echo
-
-set -ex
-exec ${personality} -- "$@"
diff --git a/containers/unit-tests/setup.sh b/containers/unit-tests/setup.sh
deleted file mode 100755
index 24764675438d..000000000000
--- a/containers/unit-tests/setup.sh
+++ /dev/null
@@ -1,79 +0,0 @@
-#!/bin/sh -ex
-
-dependencies="\
-    appstream-util \
-    autoconf \
-    automake \
-    build-essential \
-    clang \
-    curl \
-    dbus \
-    firefox-esr \
-    flake8 \
-    gcc-multilib \
-    gdb \
-    git \
-    glib-networking \
-    glib-networking-dbgsym\
-    gtk-doc-tools \
-    gettext \
-    libc6-dbg \
-    libfontconfig1 \
-    libglib2.0-0-dbgsym \
-    libglib2.0-dev \
-    libgnutls28-dev \
-    libjavascript-minifier-xs-perl \
-    libjson-glib-dev \
-    libjson-perl \
-    libkrb5-dev \
-    libpam0g-dev \
-    libpcp-import1-dev \
-    libpcp-pmda3-dev \
-    libpcp3-dev \
-    libpolkit-agent-1-dev \
-    libpolkit-gobject-1-dev \
-    libssh-4-dbgsym \
-    libssh-dev \
-    libsystemd-dev \
-    mypy \
-    npm \
-    nodejs \
-    pkg-config \
-    python3 \
-    python3-mypy \
-    python3-pip \
-    python3-pytest-asyncio \
-    python3-pytest-cov \
-    python3-pytest-timeout \
-    ssh \
-    strace \
-    valgrind \
-    vulture \
-    xmlto \
-    xsltproc \
-"
-
-echo "deb http://deb.debian.org/debian-debug/ testing-debug main" > /etc/apt/sources.list.d/ddebs.list
-echo "deb http://deb.debian.org/debian-debug/ testing-proposed-updates-debug main" >> /etc/apt/sources.list.d/ddebs.list
-apt-get update
-apt-get install -y --no-install-recommends eatmydata
-DEBIAN_FRONTEND=noninteractive eatmydata apt-get install -y --no-install-recommends ${dependencies}
-
-# https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=1057968
-echo "deb http://deb.debian.org/debian unstable main" > /etc/apt/sources.list.d/unstable.list
-apt-get update
-apt-get install -y --no-install-recommends python3-flake8
-rm /etc/apt/sources.list.d/unstable.list
-
-adduser --gecos "Builder" builder
-
-if [ "$(uname -m)" = "x86_64" ] ; then
-    # See https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=1030835
-    pip install --break-system-packages ruff
-fi
-
-# minimize image
-# useful command: dpkg-query --show -f '${package} ${installed-size}\n' | sort -k2n
-dpkg -P --force-depends libgl1-mesa-dri libglx-mesa0 perl
-
-rm -rf /var/cache/apt /var/lib/apt /var/log/* /usr/share/doc/ /usr/share/man/ /usr/share/help /usr/share/info
diff --git a/containers/unit-tests/start b/containers/unit-tests/start
deleted file mode 100755
index e01cb66370ad..000000000000
--- a/containers/unit-tests/start
+++ /dev/null
@@ -1,190 +0,0 @@
-#!/usr/bin/python3
-
-# This file is part of Cockpit.
-#
-# Copyright (C) 2022 Red Hat, Inc.
-#
-# This program is free software: you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation, either version 3 of the License, or
-# (at your option) any later version.
-#
-# This program is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-# GNU General Public License for more details.
-#
-# You should have received a copy of the GNU General Public License
-# along with this program.  If not, see <http://www.gnu.org/licenses/>.
-
-import argparse
-import os
-import shlex
-import sys
-import tempfile
-from subprocess import run
-
-
-def logged(func):
-    def wrapper(args, **kwargs):
-        print('+', shlex.join(args))
-        return func(args, **kwargs)
-    return wrapper
-
-
-def git(*args):
-    run(['git', *args], check=True)
-
-
-def git_output(*args):
-    return run(['git', *args], check=True, capture_output=True, text=True).stdout.strip()
-
-
-def podman(*args, check=True):
-    if os.path.exists('/run/.toolboxenv'):
-        cmd = ['flatpak-spawn', '--host', 'podman', *args]
-    else:
-        cmd = ['podman', *args]
-
-    return run(cmd, check=check)
-
-
-class PodmanTemporaryDirectory(tempfile.TemporaryDirectory):
-    """TemporaryDirectory subclass capable of removing files owned by subuids"""
-    @classmethod
-    def _rmtree(cls, name, ignore_errors=False):  # noqa: FBT002
-        del ignore_errors  # can't remove or rename this kwarg
-        podman('unshare', 'rm', '-r', name)
-
-    def __enter__(self):
-        # Override the TemporaryDirectory behaviour of returning its name here
-        return self
-
-
-class SourceDirectory(PodmanTemporaryDirectory):
-    def __init__(self):
-        super().__init__(prefix='cockpit-source.')
-
-    def prepare(self, args):
-        if args.branch:
-            opts = ['-c', 'advice.detachedHead=false', '-b', args.branch]
-        else:
-            opts = []
-
-        git('clone', '--recurse-submodule=vendor/*', *opts, '.', self.name)
-
-        if not args.head and not args.branch:
-            if stash := git_output('stash', 'create'):
-                git('-C', self.name, 'fetch', '--quiet', '--no-write-fetch-head', 'origin', stash)
-                git('-C', self.name, 'stash', 'apply', stash)
-
-        if not args.no_node_modules:
-            run([f'{self.name}/tools/node-modules', 'checkout'], check=True)
-
-
-class ResultsDirectory(PodmanTemporaryDirectory):
-    def __init__(self):
-        super().__init__(prefix='cockpit-results.')
-
-    def copy_out(self, destination):
-        podman('unshare', 'cp', '-rT', self.name, destination)
-
-
-def main():
-    parser = argparse.ArgumentParser()
-    parser.add_argument('--verbose', '-v', action='store_true', help='Show commands when running them')
-    parser.add_argument('--results', metavar='DIRECTORY', help="Copy container /results to the given host directory")
-
-    group = parser.add_argument_group(title='Container options')
-    group.add_argument('--image', default='ghcr.io/cockpit-project/unit-tests', help='Container image to use')
-    group.add_argument('--image-tag', default='latest', help='Container image tag to use')
-    group.add_argument('--env', metavar='NAME=VAL', action='append', default=[],
-                       help='Set an environment variable in the container')
-    group.add_argument('--network', action="store_true",
-                       help="Enable network in the container (default: disabled)")
-    group.add_argument('--interactive', '-i', action="store_true",
-                       help="Interactive mode (implied by no command or script)")
-    group.add_argument('--tty', '-t', action="store_true",
-                       help="Allocate a pseudoterminal (implied by no command or script)")
-    group.add_argument('--user', help="Pass through the --user flag to podman")
-    group.add_argument('--entrypoint', metavar='CMD', help="Provide the --entrypoint flag to podman")
-    group.add_argument('--workdir', help="Provide the --workdir flag to podman")
-
-    group = parser.add_argument_group(title='What to build').add_mutually_exclusive_group()
-    group.add_argument('--head', action='store_true', help='Build the HEAD commit')
-    group.add_argument('-b', dest='branch', metavar='NAME', help='Build the named branch or tag')
-    group.add_argument('--work-tree', action='store_true',
-                       help='Build the HEAD commit, plus changes on the filesystem (default)')
-
-    group = parser.add_argument_group(title='Preparation').add_mutually_exclusive_group()
-    group.add_argument('--no-node-modules', action='store_true',
-                       help='Disable checking out node_modules/ during preparation')
-
-    group = parser.add_argument_group(title='Command to run').add_mutually_exclusive_group()
-    group.add_argument('-c', metavar='SCRIPT', dest='script', help="Run the provided shell script")
-    group.add_argument('--make-dist', action='store_true', help='Run `make dist`.  Requires --results.')
-    group.add_argument('--make', metavar='TARGET', help='Run `make` on the given target')
-    # re: default=[]: https://github.com/python/cpython/issues/86020
-    group.add_argument('command', metavar='CMD', nargs='*', default=[], help="Run a normal command, with arguments")
-
-    args = parser.parse_args()
-
-    if args.results and os.path.exists(args.results):
-        parser.error(f'--results directory `{args.results}` already exists')
-
-    if args.make_dist and not args.results:
-        parser.error('--make-dist requires --results directory')
-
-    if args.verbose:
-        global run
-        run = logged(run)
-
-    with SourceDirectory() as source_dir, ResultsDirectory() as results_dir:
-        options = {
-            '--rm',
-            '--log-driver=none',
-            f'--volume={source_dir.name}:/source:Z,U',
-        }
-
-        if args.results:
-            options.add(f'--volume={results_dir.name}:/results:Z,U')
-
-        if not args.network:
-            options.add('--network=none')
-        if args.user:
-            options.add(f'--user={args.user}')
-        if args.entrypoint:
-            options.add(f'--entrypoint={args.entrypoint}')
-        if args.workdir:
-            options.add(f'--workdir={args.workdir}')
-        if args.interactive:
-            options.add('--interactive')
-        if args.tty:
-            options.add('--tty')
-        for keyval in args.env:
-            options.add(f'--env={keyval}')
-
-        command = []
-        if args.command:
-            command = args.command
-        elif args.script:
-            command = ['sh', '-c', args.script]
-        elif args.make:
-            command = ['sh', '-c', '/source/autogen.sh; exec make -j$(nproc) ' + shlex.quote(args.make)]
-        elif args.make_dist:
-            command = ['sh', '-c', 'cp -t /results $(/source/tools/make-dist)']
-        else:
-            options.update(['--tty', '--interactive'])
-
-        source_dir.prepare(args)
-
-        result = podman('run', *options, f'{args.image}:{args.image_tag}', *command)
-
-        if result.returncode == 0 and args.results:
-            results_dir.copy_out(args.results)
-
-        return result.returncode
-
-
-if __name__ == '__main__':
-    sys.exit(main())