diff --git a/.github/workflows/ci-cd.yml b/.github/workflows/ci-cd.yml
index 5b450d6bf..e2994099d 100644
--- a/.github/workflows/ci-cd.yml
+++ b/.github/workflows/ci-cd.yml
@@ -675,83 +675,28 @@ jobs:
           !fromJSON(needs.pre-setup.outputs.is-untagged-devel)
           && !fromJSON(needs.pre-setup.outputs.release-requested)
         ) && 'test' || ''
-      }}] manylinux
+      }}] manylinux [tested]
     needs:
     - build-src
     - pre-setup  # transitive, for accessing settings
-    strategy:
-      matrix:
-        manylinux-python-target:
-        # NOTE: Must be from this list:
-        # NOTE: $ podman run -it --rm \
-        # NOTE:   quay.io/pypa/manylinux2014_x86_64 \
-        # NOTE:   ls -1 /opt/python
-        - cp38-cp38
-        - cp39-cp39
-        - cp310-cp310
-        - cp311-cp311
-        - cp312-cp312
-        manylinux-year-target:
-        - 2014
-        - _2_24
-        - _2_28
-        manylinux-image-target:
-        # NOTE: Keep in sync with `build-manylinux-container-images.yml`.
-        # NOTE: Ordered from "heavy" to "fast".
-        - arch: x86_64
-          qemu_arch: amd64
-        include:
-        # NOTE: manylinux2010 only on x86_64
-        - manylinux-python-target: cp38-cp38
-          manylinux-image-target:
-            arch: x86_64
-            qemu_arch: amd64
-          manylinux-year-target: 2010
-        - manylinux-python-target: cp39-cp39
-          manylinux-image-target:
-            arch: x86_64
-            qemu_arch: amd64
-          manylinux-year-target: 2010
-        - manylinux-python-target: cp310-cp310
-          manylinux-image-target:
-            arch: x86_64
-            qemu_arch: amd64
-          manylinux-year-target: 2010
-        # NOTE: manylinux1 caps out at Python 3.9
-        - manylinux-python-target: cp38-cp38
-          manylinux-image-target:
-            arch: x86_64
-            qemu_arch: amd64
-          manylinux-year-target: 1
-        - manylinux-python-target: cp39-cp39
-          manylinux-image-target:
-            arch: x86_64
-            qemu_arch: amd64
-          manylinux-year-target: 1
-        exclude:
-        # NOTE: cp312-cp312 unavailable before _2_28
-        - manylinux-python-target: cp312-cp312
-          manylinux-year-target: 2014
-        - manylinux-python-target: cp312-cp312
-          manylinux-year-target: _2_24
-
-    uses: ./.github/workflows/reusable-build-wheel.yml
+    uses: ./.github/workflows/reusable-cibuildwheel.yml
     with:
-      # qemu: ${{ matrix.qemu }}
+      os: ubuntu-latest
+      wheel-tags-to-skip: >-
+        *_i686
+        *-musllinux_*
+        *-*linux_{aarch64,ppc64le,s390x}
+        pp*
       source-tarball-name: >-
         ${{ needs.pre-setup.outputs.sdist-artifact-name }}
       dists-artifact-name: >-
         ${{ needs.pre-setup.outputs.dists-artifact-name }}
-      wheel-artifact-name: ${{ needs.pre-setup.outputs.wheel-artifact-name }}
-      cache-key-files: ${{ needs.pre-setup.outputs.cache-key-files }}
-      release-requested: >-
-        ${{ needs.pre-setup.outputs.release-requested }}
-      manylinux-python-target: ${{ matrix.manylinux-python-target }}
-      manylinux-year-target: ${{ matrix.manylinux-year-target }}
-      manylinux-image-target-arch: >-
-        ${{ matrix.manylinux-image-target.arch }}
-      manylinux-image-target-qemu-arch: >-
-        ${{ matrix.manylinux-image-target.qemu_arch }}
+      cython-tracing: >-  # Cython line tracing for coverage collection
+        ${{
+          fromJSON(needs.pre-setup.outputs.profiling-enabled)
+          && 'true'
+          || 'false'
+        }}
 
   build-bin-manylinux-odd-arches:
     name: >-
@@ -767,57 +712,29 @@ jobs:
           !fromJSON(needs.pre-setup.outputs.is-untagged-devel)
           && !fromJSON(needs.pre-setup.outputs.release-requested)
         ) && 'test' || ''
-      }}] manylinux
+      }}] manylinux [odd]
     needs:
     - build-src
     - pre-setup  # transitive, for accessing settings
-    strategy:
-      matrix:
-        manylinux-python-target:
-        # NOTE: Must be from this list:
-        # NOTE: $ podman run -it --rm \
-        # NOTE:   quay.io/pypa/manylinux2014_x86_64 \
-        # NOTE:   ls -1 /opt/python
-        - cp38-cp38
-        - cp39-cp39
-        - cp310-cp310
-        - cp311-cp311
-        - cp312-cp312
-        manylinux-year-target:
-        - 2014
-        - _2_24
-        - _2_28
-        manylinux-image-target:
-        # NOTE: Keep in sync with `build-manylinux-container-images.yml`.
-        # NOTE: Ordered from "heavy" to "fast".
-        - arch: aarch64
-          qemu_arch: arm64
-        - arch: s390x
-        - arch: ppc64le
-        exclude:
-        # NOTE: cp312-cp312 unavailable before _2_28
-        - manylinux-python-target: cp312-cp312
-          manylinux-year-target: 2014
-        - manylinux-python-target: cp312-cp312
-          manylinux-year-target: _2_24
-
-    uses: ./.github/workflows/reusable-build-wheel.yml
+    uses: ./.github/workflows/reusable-cibuildwheel.yml
     with:
-      # qemu: ${{ matrix.qemu }}
+      os: ubuntu-latest
+      wheel-tags-to-skip: >-
+        *_i686
+        *-musllinux_*
+        *-*linux_x86_64
+        pp*
       source-tarball-name: >-
         ${{ needs.pre-setup.outputs.sdist-artifact-name }}
       dists-artifact-name: >-
         ${{ needs.pre-setup.outputs.dists-artifact-name }}
-      wheel-artifact-name: ${{ needs.pre-setup.outputs.wheel-artifact-name }}
-      cache-key-files: ${{ needs.pre-setup.outputs.cache-key-files }}
-      release-requested: >-
-        ${{ needs.pre-setup.outputs.release-requested }}
-      manylinux-python-target: ${{ matrix.manylinux-python-target }}
-      manylinux-year-target: ${{ matrix.manylinux-year-target }}
-      manylinux-image-target-arch: >-
-        ${{ matrix.manylinux-image-target.arch }}
-      manylinux-image-target-qemu-arch: >-
-        ${{ matrix.manylinux-image-target.qemu_arch }}
+      qemu: all
+      cython-tracing: >-  # Cython line tracing for coverage collection
+        ${{
+          fromJSON(needs.pre-setup.outputs.profiling-enabled)
+          && 'true'
+          || 'false'
+        }}
 
   build-src:
     name: >-
diff --git a/.github/workflows/reusable-build-wheel.yml b/.github/workflows/reusable-build-wheel.yml
deleted file mode 100644
index d47548a2a..000000000
--- a/.github/workflows/reusable-build-wheel.yml
+++ /dev/null
@@ -1,223 +0,0 @@
----
-
-name: ♲  👷 Build wheel 🛞📦
-
-on:  # yamllint disable-line rule:truthy
-  workflow_call:
-    inputs:
-      dists-artifact-name:
-        description: Workflow artifact name containing dists
-        required: true
-        type: string
-      cython-tracing:
-        description: Whether to build Cython modules with line tracing
-        default: '0'
-        required: false
-        type: string
-      # os:
-      #   description: VM OS to use, without version suffix
-      #   default: ubuntu
-      #   required: false
-      #   type: string
-      # qemu:
-      #   description: Emulated QEMU architecture
-      #   default: ''
-      #   required: false
-      #   type: string
-      source-tarball-name:
-        description: Sdist filename wildcard
-        required: true
-        type: string
-      # wheel-tags-to-skip:
-      #   description: Wheel tags to skip building
-      #   default: ''
-      #   required: false
-      #   type: string
-      manylinux-python-target:
-        description: A Python version present in a manylinux container image
-        required: true
-        type: string
-      manylinux-year-target:
-        description: Manylinux container image name suffix
-        required: true
-        type: string
-      manylinux-image-target-arch:
-        description: Architecture of a wheel to be made
-        required: true
-        type: string
-      manylinux-image-target-qemu-arch:
-        description: QEMU-emulated architecture for the wheel
-        required: true
-        type: string
-      cache-key-files:
-        description: Dependency files cache
-        required: true
-        type: string
-      release-requested:
-        description: Flag whether this is CI run is a release request
-        default: 'false'
-        required: false
-        type: string
-      wheel-artifact-name:
-        description: Wheel filename wildcard
-        default: ''
-        required: false
-        type: string
-
-env:
-  FORCE_COLOR: "1"  # Make tools pretty.
-  PIP_DISABLE_PIP_VERSION_CHECK: "1"
-  PIP_NO_PYTHON_VERSION_WARNING: "1"
-  TOX_VERSION: tox < 4.12
-
-jobs:
-
-  build-wheel:
-    name: >-
-      ${{ inputs.manylinux-year-target }}-${{
-        inputs.manylinux-image-target-arch }}
-      🐍 ${{ inputs.manylinux-python-target }}
-    runs-on: ubuntu-latest
-
-    env:
-      ANSIBLE_PYLIBSSH_CYTHON_TRACING: ${{ inputs.cython-tracing }}
-      DOCKER_EXECUTABLE: podman
-      QEMU_ARCH: >-
-        ${{
-          inputs.manylinux-image-target.qemu-arch
-          || inputs.manylinux-image-target-arch
-        }}
-      TOXENV: >-
-        build-dists-manylinux${{ inputs.manylinux-year-target
-        }}-${{ inputs.manylinux-image-target-arch }},metadata-validation
-
-    steps:
-    - name: Compute GHA artifact name ending
-      id: gha-artifact-name
-      run: |
-        from hashlib import sha512
-        from os import environ
-        from pathlib import Path
-
-        FILE_APPEND_MODE = 'a'
-
-        inputs_json_str = """${{ toJSON(inputs) }}"""
-
-        hash = sha512(inputs_json_str.encode()).hexdigest()
-
-        with Path(environ['GITHUB_OUTPUT']).open(
-                mode=FILE_APPEND_MODE,
-        ) as outputs_file:
-            print(f'hash={hash}', file=outputs_file)
-      shell: python
-
-    - name: Switch to using Python 3.11 by default
-      uses: actions/setup-python@v5.3.0
-      with:
-        python-version: 3.11
-
-    - name: Retrieve the project source from an sdist inside the GHA artifact
-      uses: re-actors/checkout-python-sdist@release/v2
-      with:
-        source-tarball-name: ${{ inputs.source-tarball-name }}
-        workflow-artifact-name: ${{ inputs.dists-artifact-name }}
-
-    - name: >-
-        Calculate Python interpreter version hash value
-        for use in the cache key
-      id: calc-cache-key-py
-      run: |
-        from hashlib import sha512
-        from os import environ
-        from pathlib import Path
-        from sys import version
-
-        FILE_APPEND_MODE = 'a'
-
-        hash = sha512(version.encode()).hexdigest()
-
-        with Path(environ['GITHUB_OUTPUT']).open(
-                mode=FILE_APPEND_MODE,
-        ) as outputs_file:
-            print(f'py-hash-key={hash}', file=outputs_file)
-      shell: python
-    - name: Set up pip cache
-      uses: actions/cache@v4
-      with:
-        path: >-
-          ${{
-              runner.os == 'Linux'
-              && '~/.cache/pip'
-              || '~/Library/Caches/pip'
-          }}
-        key: >-
-          ${{ runner.os }}-pip-${{
-          steps.calc-cache-key-py.outputs.py-hash-key }}-${{
-          inputs.cache-key-files }}
-        restore-keys: |
-          ${{ runner.os }}-pip-${{
-            steps.calc-cache-key-py.outputs.py-hash-key
-          }}-
-          ${{ runner.os }}-pip-
-          ${{ runner.os }}-
-    - name: Install tox
-      run: >-
-        python -m
-        pip install
-        --user
-        '${{ env.TOX_VERSION }}'
-
-    - name: Pre-populate the tox env
-      run: >-
-        python -m
-        tox
-        --parallel auto
-        --parallel-live
-        --skip-missing-interpreters false
-        --notest
-
-    - name: >-
-        Set up QEMU ${{ env.QEMU_ARCH }} arch emulation
-        with Podman
-      if: env.QEMU_ARCH != 'amd64'
-      run: >-
-        sudo podman run
-        --rm --privileged
-        multiarch/qemu-user-static
-        --reset -p yes
-
-    - name: >-
-        Build ${{ inputs.manylinux-python-target }} dist
-        and verify wheel metadata
-      run: >-
-        python -m
-        tox
-        --parallel auto
-        --parallel-live
-        --skip-missing-interpreters false
-        --skip-pkg-install
-        --
-        ${{ inputs.manylinux-python-target }}
-    - name: Verify that the artifacts with expected names got created
-      run: >-
-        ls -1
-        dist/${{ inputs.wheel-artifact-name }}
-    - name: Store ${{ inputs.manylinux-python-target }} binary wheel
-      uses: actions/upload-artifact@v4
-      with:
-        name: ${{ inputs.dists-artifact-name }}-
-          ${{ inputs.manylinux-year-target }}-
-          ${{ inputs.manylinux-image-target-arch }}-
-          ${{ inputs.manylinux-image-target-qemu-arch }}-
-          ${{ inputs.manylinux-python-target }}-
-          ${{ steps.gha-artifact-name.outputs.hash }}
-        # NOTE: Exact expected file names are specified here
-        # NOTE: as a safety measure — if anything weird ends
-        # NOTE: up being in this dir or not all dists will be
-        # NOTE: produced, this will fail the workflow.
-        path: |
-          dist/${{ inputs.wheel-artifact-name }}
-        retention-days: >-
-          ${{ fromJSON(inputs.release-requested) && 7 || 4 }}
-
-...
diff --git a/.github/workflows/reusable-cibuildwheel.yml b/.github/workflows/reusable-cibuildwheel.yml
index 3007a6319..7672a8150 100644
--- a/.github/workflows/reusable-cibuildwheel.yml
+++ b/.github/workflows/reusable-cibuildwheel.yml
@@ -53,7 +53,7 @@ jobs:
         || format('Build wheels on {0} {1}', inputs.os, inputs.qemu)
       }}
     runs-on: ${{ inputs.os }}
-    timeout-minutes: ${{ inputs.qemu && 60 || 8 }}
+    timeout-minutes: ${{ inputs.qemu && 70 || 8 }}
     steps:
     - name: Compute GHA artifact name ending
       id: gha-artifact-name
diff --git a/build-scripts/build-all-manylinux-wheels.sh b/build-scripts/build-all-manylinux-wheels.sh
deleted file mode 100755
index ba05f3877..000000000
--- a/build-scripts/build-all-manylinux-wheels.sh
+++ /dev/null
@@ -1,41 +0,0 @@
-#! /usr/bin/env bash
-if [ -n "$DEBUG" ]
-then
-    set -x
-fi
-
-set -Eeuo pipefail
-
-manylinux1_image_prefix="quay.io/pypa/manylinux1_"
-manylinux1_image_prefix="pyca/cryptography-manylinux1:"
-manylinux1_image_prefix="ghcr.io/pyca/cryptography-manylinux1:"
-#manylinux1_image_prefix="quay.io/pypa/manylinux2010_"
-#manylinux1_image_prefix="pyca/cryptography-manylinux2010:"
-dock_ext_args=""
-declare -A docker_pull_pids=()  # This syntax requires at least bash v4
-
-for arch in x86_64
-do
-    #docker pull "${manylinux1_image_prefix}${arch}" &
-    podman pull "${manylinux1_image_prefix}${arch}" &
-    docker_pull_pids[$arch]=$!
-done
-
-for arch in x86_64
-do
-    echo
-    echo
-    arch_pull_pid=${docker_pull_pids[$arch]}
-    echo Waiting for docker pull PID $arch_pull_pid to complete downloading container for $arch arch...
-    wait $arch_pull_pid  # await for docker image for current arch to be pulled from hub
-    [ $arch == "i686" ] && dock_ext_args="linux32"
-
-    echo Building wheel for $arch arch
-    #docker run --rm -v `pwd`:/io "${manylinux1_image_prefix}${arch}" $dock_ext_args /io/build-scripts/build-manylinux-wheels.sh "$LIBSSH_VERSION" &
-    podman run --rm -v `pwd`:/io "${manylinux1_image_prefix}${arch}" $dock_ext_args /io/build-scripts/build-manylinux-wheels.sh &
-
-    dock_ext_args=""  # Reset docker args, just in case
-done
-wait
-
-set +u
diff --git a/build-scripts/build-manylinux-wheels.sh b/build-scripts/build-manylinux-wheels.sh
deleted file mode 100755
index 22acf407e..000000000
--- a/build-scripts/build-manylinux-wheels.sh
+++ /dev/null
@@ -1,247 +0,0 @@
-#!/usr/bin/env bash
-
-DEBUG=$DEBUG
-
-if [ -n "$DEBUG" ]
-then
-    set -x
-fi
-
-MANYLINUX_TARGET="${1}"
-PYTHON_TARGET="${2}"
-
-set -Eeuo pipefail
-
-THIS_SCRIPT_DIR_PATH=$(dirname "$(readlink -m $(type -p "${0}"))")
-IMAGE_SCRIPTS_DIR_PATH="${THIS_SCRIPT_DIR_PATH}/manylinux-container-image"
-
-source "${IMAGE_SCRIPTS_DIR_PATH}/get-static-deps-dir.sh"
-source "${IMAGE_SCRIPTS_DIR_PATH}/activate-userspace-tools.sh"
-
-SRC_DIR=/io
-GIT_DIR="${SRC_DIR}/.git"
-PERM_REF_HOST_FILE="${SRC_DIR}/setup.cfg"
-PEP517_CONFIG_FILE="${SRC_DIR}/pyproject.toml"
-DIST_NAME="$(cat "${PERM_REF_HOST_FILE}" | grep '^name = ' | awk '{print$3}' | sed s/-/_/)"
-IMPORTABLE_PKG="$(ls --ignore='*.egg-info' "${SRC_DIR}/src/")"  # must contain only one dir
-
->&2 echo Verifying that $IMPORTABLE_PKG can be the target package...
->/dev/null stat ${SRC_DIR}/src/${IMPORTABLE_PKG}/*.p{y,yx,xd}
-
-PYTHONS="$(ls -1 --ignore=cp34-cp34m /opt/python/ | sort -r)"
-if [ -n "${PYTHON_TARGET}" ]
-then
-    if &>/dev/null grep -ow "^${PYTHON_TARGET}$" <<<"$PYTHONS"
-    then
-        >&2 echo Using the target Python requested \
-            by the second argument ${PYTHON_TARGET}
-        PYTHONS="${PYTHON_TARGET}"
-    else
-        >&2 echo Invalid Python target requested \
-            by the second CLI argument ${PYTHON_TARGET}
-        exit 1
-    fi
-else
-    >&2 echo Using all Python targets found in this env
-fi
-
->&2 echo Selected Python targets for this build run:
-echo "${PYTHONS}" | >&2 tr ' ' '\n'
-
-
-MANYLINUX_TAG="$(
-    /opt/python/cp39-cp39/bin/python \
-    "${IMAGE_SCRIPTS_DIR_PATH}/manylinux_mapping.py" \
-    "${MANYLINUX_TARGET}"
-)"
-
-
-# Avoid creation of __pycache__/*.py[c|o]
-export PYTHONDONTWRITEBYTECODE=1
-
-import_userspace_tools
-
-PIP_GLOBAL_ARGS=
-if [ -n "$DEBUG" ]
-then
-    PIP_GLOBAL_ARGS=-vv
-fi
-GIT_GLOBAL_ARGS="--git-dir=${GIT_DIR} --work-tree=${SRC_DIR}"
-TESTS_SRC_DIR="${SRC_DIR}/tests"
-BUILD_DIR=$(mktemp -d "/tmp/${DIST_NAME}-${MANYLINUX_TAG}-build.XXXXXXXXXX")
-TESTS_DIR="${BUILD_DIR}/tests"
-STATIC_DEPS_PREFIX="$(get_static_deps_dir)"
-
-ORIG_WHEEL_DIR="${BUILD_DIR}/original-wheelhouse"
-WHEEL_DEP_DIR="${BUILD_DIR}/deps-wheelhouse"
-MANYLINUX_DIR="${BUILD_DIR}/manylinux-wheelhouse"
-WHEELHOUSE_DIR="${SRC_DIR}/dist"
-UNPACKED_WHEELS_DIR="${BUILD_DIR}/unpacked-wheels"
-VENVS_DIR="${BUILD_DIR}/venvs"
-ISOLATED_SRC_DIRS="${BUILD_DIR}/src"
-
-# NOTE: `LDFLAGS` is necessary for the C-extension build's linker to
-# NOTE: locate the symbols in the libssh shared object files.
-# NOTE: Otherwise, the error is:
-#
-#   gcc -pthread -shared -lssh -I/opt/manylinux-static-deps.PPkLKziXI7/include -DCYTHON_TRACE=1 -DCYTHON_TRACE_NOGIL=1 /tmp/pip-req-build-4h841og7/src/tmpy3l03tmj/tmp/pip-req-build-4h841og7/src/pylibsshext/session.o -lssh -o build/lib.linux-x86_64-3.9/pylibsshext/session.cpython-39-x86_64-linux-gnu.so
-#   /opt/rh/devtoolset-2/root/usr/libexec/gcc/x86_64-CentOS-linux/4.8.2/ld: cannot find -lssh
-#   /opt/rh/devtoolset-2/root/usr/libexec/gcc/x86_64-CentOS-linux/4.8.2/ld: cannot find -lssh
-#   collect2: error: ld returned 1 exit status
-#   error: command '/opt/rh/devtoolset-2/root/usr/bin/gcc' failed with exit code 1
-#   ----------------------------------------
-#   ERROR: Failed building wheel for ansible-pylibssh
-# Failed to build ansible-pylibssh
-# ERROR: Failed to build one or more wheels
-export LDFLAGS="'-L${STATIC_DEPS_PREFIX}/lib64' '-L${STATIC_DEPS_PREFIX}/lib'"
-
-# NOTE: `LD_LIBRARY_PATH` is necessary so that `auditwheel repair` could locate `libssh.so.4`
-export LD_LIBRARY_PATH="${STATIC_DEPS_PREFIX}/lib64:${STATIC_DEPS_PREFIX}/lib:$LD_LIBRARY_PATH"
-
-ARCH=`uname -m`
-
->&2 echo
->&2 echo
->&2 echo ===============================================
->&2 echo Copying the source repo to temporary locations:
->&2 echo ===============================================
->&2 echo
-for PY in $PYTHONS; do
-    >&2 echo Creating "${ISOLATED_SRC_DIRS}/${PY}"...
-    if [ -d "${GIT_DIR}" ]
-    then
-        # NOTE: Allow `setuptools-scm` grab the version from Git
-        git ${GIT_GLOBAL_ARGS} worktree add --detach \
-          "${ISOLATED_SRC_DIRS}/${PY}"
-        cp -v "${PEP517_CONFIG_FILE}" "${ISOLATED_SRC_DIRS}/${PY}"/
-    else
-        # NOTE: Rely on `.git_archival.txt` for versioning
-        mkdir -pv "${ISOLATED_SRC_DIRS}/"
-        cp -a "${SRC_DIR}" "${ISOLATED_SRC_DIRS}/${PY}"
-    fi
-done
-
->&2 echo
->&2 echo
->&2 echo ================
->&2 echo Building wheels:
->&2 echo ================
->&2 echo
-export CFLAGS="'-I${STATIC_DEPS_PREFIX}/include'"
-for PY in $PYTHONS; do
-    PIP_BIN="/opt/python/${PY}/bin/pip"
-    >&2 echo Using "${PIP_BIN}"...
-    ${PIP_BIN} install -U 'pip >= 20' wheel ${PIP_GLOBAL_ARGS}
-    ${PIP_BIN} wheel "${ISOLATED_SRC_DIRS}/${PY}" -w "${ORIG_WHEEL_DIR}" ${PIP_GLOBAL_ARGS}
-done
-
->&2 echo
->&2 echo
->&2 echo ================
->&2 echo Reparing wheels:
->&2 echo ================
->&2 echo
-# Bundle external shared libraries into the wheels
-for PY in $PYTHONS; do
-    for whl in ${ORIG_WHEEL_DIR}/${DIST_NAME}-*-${PY}-linux_${ARCH}.whl; do
-        >&2 echo Reparing "${whl}" for "${MANYLINUX_TAG}"...
-        auditwheel repair --only-plat --plat "${MANYLINUX_TARGET}" "${whl}" -w ${MANYLINUX_DIR}
-    done
-done
-
-# Download deps
->&2 echo
->&2 echo
->&2 echo =========================
->&2 echo Downloading dependencies:
->&2 echo =========================
->&2 echo
-for PY in $PYTHONS; do
-    for WHEEL_FILE in `ls ${MANYLINUX_DIR}/${DIST_NAME}-*-${PY}-${MANYLINUX_TAG}.whl`; do
-        PIP_BIN="/opt/python/${PY}/bin/pip"
-        >&2 echo Downloading ${WHEEL_FILE} deps using ${PIP_BIN}...
-        ${PIP_BIN} download -d "${WHEEL_DEP_DIR}" "${WHEEL_FILE}" ${PIP_GLOBAL_ARGS}
-    done
-done
-
->&2 echo
->&2 echo ===================
->&2 echo Creating test venvs
->&2 echo ===================
->&2 echo
-for PY in $PYTHONS; do
-    VENV_NAME="${PY}-${MANYLINUX_TAG}"
-    VENV_PATH="${VENVS_DIR}/${VENV_NAME}"
-    VENV_BIN="/opt/python/${PY}/bin/virtualenv"
-
-    >&2 echo
-    >&2 echo Creating a venv at ${VENV_PATH}...
-    ${VENV_BIN} "${VENV_PATH}"
-done
-
-# Install packages
->&2 echo
->&2 echo
->&2 echo ============================
->&2 echo Testing wheels installation:
->&2 echo ============================
->&2 echo
-for PY in $PYTHONS; do
-    VENV_NAME="${PY}-${MANYLINUX_TAG}"
-    VENV_PATH="${VENVS_DIR}/${VENV_NAME}"
-    PIP_BIN="${VENV_PATH}/bin/pip"
-    >&2 echo Using ${PIP_BIN}...
-    ${PIP_BIN} install --no-compile "${DIST_NAME}" --no-index -f "${MANYLINUX_DIR}/" ${PIP_GLOBAL_ARGS}
-done
-
->&2 echo
->&2 echo ==============
->&2 echo WHEEL ANALYSIS
->&2 echo ==============
->&2 echo
-for PY in $PYTHONS; do
-    WHEEL_BIN="/opt/python/${PY}/bin/wheel"
-    PLAT_TAG="${PY}-${MANYLINUX_TAG}"
-    UNPACKED_DIR=${UNPACKED_WHEELS_DIR}/${PLAT_TAG}
-    WHEEL_FILE=`ls ${MANYLINUX_DIR}/${DIST_NAME}-*-${PLAT_TAG}.whl`
-    >&2 echo
-    >&2 echo Analysing ${WHEEL_FILE}...
-    auditwheel show "${WHEEL_FILE}"
-    ${WHEEL_BIN} unpack -d "${UNPACKED_DIR}" "${WHEEL_FILE}"
-    # chmod avoids ldd warning about files being non-executable:
-    chmod +x "${UNPACKED_DIR}"/${DIST_NAME}-*/{${DIST_NAME}.libs/*.so.*,${IMPORTABLE_PKG}/*.so}
-    >&2 echo Verifying that all links in '`*.so`' files of ${WHEEL_FILE} exist...
-    ! ldd "${UNPACKED_DIR}"/${DIST_NAME}-*/{${DIST_NAME}.libs/*.so.*,${IMPORTABLE_PKG}/*.so} | grep '=> not found'
-done
-
->&2 echo
->&2 echo
->&2 echo ===================================
->&2 echo Running smoke tests against wheels:
->&2 echo ===================================
->&2 echo
-cp -vr "${TESTS_SRC_DIR}" "${TESTS_DIR}"
-sed \
-  's#\s\+--cov.*##;s#\s\+--no-cov-on-fail.*##;s#\s\+-p\spytest_cov.*##' \
-  "${SRC_DIR}/pytest.ini" > "${TESTS_DIR}/pytest.ini"
-pushd "${TESTS_DIR}"
-for PY_BIN in `ls ${VENVS_DIR}/*/bin/python`; do
-    $PY_BIN -B -m pip install --no-compile pytest pytest-forked pytest-xdist ${PIP_GLOBAL_ARGS}
-    $PY_BIN -B -m pytest -m smoke "${TESTS_DIR}"
-done
-popd
-
->&2 echo
->&2 echo
->&2 echo ==================
->&2 echo SELF-TEST COMPLETE
->&2 echo ==================
->&2 echo
-
->&2 echo Copying built manylinux wheels back to the host...
-chown -R --reference="${PERM_REF_HOST_FILE}" "${MANYLINUX_DIR}"/*
-mkdir -pv "${WHEELHOUSE_DIR}"
-chown --reference="${PERM_REF_HOST_FILE}" "${WHEELHOUSE_DIR}"
-cp -av "${MANYLINUX_DIR}"/"${DIST_NAME}"-*-${MANYLINUX_TAG}.whl "${WHEELHOUSE_DIR}/"
->&2 echo Final OS-specific wheels for ${DIST_NAME}:
-ls -l ${WHEELHOUSE_DIR}
diff --git a/docs/changelog-fragments/562.breaking.rst b/docs/changelog-fragments/562.breaking.rst
new file mode 100644
index 000000000..5deced1db
--- /dev/null
+++ b/docs/changelog-fragments/562.breaking.rst
@@ -0,0 +1,4 @@
+PyPI no longer ships year-versioned manylinux wheels. One may
+have to update their version of pip to pick up the new ones.
+
+-- by :user:`webknjaz`
diff --git a/docs/changelog-fragments/562.contrib.rst b/docs/changelog-fragments/562.contrib.rst
new file mode 100644
index 000000000..b7ab0b339
--- /dev/null
+++ b/docs/changelog-fragments/562.contrib.rst
@@ -0,0 +1,4 @@
+Manylinux wheels are no longer built using custom shell scripts.
+Instead, this is delegated to the ``cibuildwheel`` tool.
+
+-- by :user:`webknjaz`
diff --git a/docs/changelog-fragments/562.packaging.rst b/docs/changelog-fragments/562.packaging.rst
new file mode 100644
index 000000000..079f0a2b0
--- /dev/null
+++ b/docs/changelog-fragments/562.packaging.rst
@@ -0,0 +1,2 @@
+PyPI now only ships :pep:`660`-compatible manylinux wheels
+-- by :user:`webknjaz`.
diff --git a/docs/installation_guide.rst b/docs/installation_guide.rst
index 5f1cd0042..72e42e951 100644
--- a/docs/installation_guide.rst
+++ b/docs/installation_guide.rst
@@ -128,10 +128,7 @@ compatible wheels, use:
 
 .. code-block:: shell-session
 
-    [dir:pylibssh] $ tox -e build-dists-manylinux1-x86_64  # with Docker
-
-    [dir:pylibssh] $ # or with Podman
-    [dir:pylibssh] $ DOCKER_EXECUTABLE=podman tox -e build-dists-manylinux1-x86_64
+    [dir:pylibssh] $ tox r -e cibuildwheel
 
 .. seealso::
 
diff --git a/pyproject.toml b/pyproject.toml
index 9ccc99803..507311cfa 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -142,6 +142,7 @@ profile = "True"
 
 [tool.cibuildwheel]
 build-frontend = "build"
+# container-engine = "podman"  # FIXME?
 test-requires = "pytest pytest-cov pytest-xdist pytest-forked"
 test-command = "python -Im pytest -m smoke --no-cov {project}/tests"
 skip = "pp*"
@@ -158,6 +159,28 @@ PIP_NO_WARN_SCRIPT_LOCATION = "1"
 PRE_COMMIT_COLOR = "always"
 PY_COLORS = "1"
 
+[tool.cibuildwheel.linux]
+manylinux-aarch64-image = "ghcr.io/ansible/pylibssh-manylinux_2_28_aarch64:libssh-v0.9.6"
+manylinux-ppc64le-image = "ghcr.io/ansible/pylibssh-manylinux_2_28_ppc64le:libssh-v0.9.6"
+manylinux-s390x-image = "ghcr.io/ansible/pylibssh-manylinux_2_28_s390x:libssh-v0.9.6"
+manylinux-x86_64-image = "ghcr.io/ansible/pylibssh-manylinux_2_28_x86_64:libssh-v0.9.6"
+skip = [
+  "*-musllinux_*",  # FIXME: musllinux needs us to provide with containers pre-built libssh
+  "pp*",  # FIXME: we don't ship these currently but could
+
+  # The support for 32-bit wheels has been dropped long ago:
+  "*-manylinux_i686",
+  "*-musllinux_i686",
+]
+
+[tool.cibuildwheel.linux.environment]
+STATIC_DEPS_DIR = "$(cat /root/.static-deps-path)"
+# LDFLAGS = "'-L${STATIC_DEPS_PREFIX}/lib64' '-L${STATIC_DEPS_PREFIX}/lib'"
+# LD_LIBRARY_PATH = "${STATIC_DEPS_PREFIX}/lib64:${STATIC_DEPS_PREFIX}/lib:${LD_LIBRARY_PATH}"
+CFLAGS="'-I$(cat /root/.static-deps-path)/include'"
+LDFLAGS = "'-L$(cat /root/.static-deps-path)/lib64' '-L$(cat /root/.static-deps-path)/lib'"
+LD_LIBRARY_PATH = "$(cat /root/.static-deps-path)/lib64:$(cat /root/.static-deps-path)/lib:${LD_LIBRARY_PATH}"
+
 [tool.cibuildwheel.macos]
 before-build = [
   "brew install libssh",  # @0.9.4  # pinning the version does not work
diff --git a/tox.ini b/tox.ini
index 3f66882a7..8003de8ed 100644
--- a/tox.ini
+++ b/tox.ini
@@ -230,7 +230,7 @@ description =
   Verify that dists under the dist/ dir have valid metadata
 depends =
   build-dists
-  build-dists-manylinux{1,2010,2014,_2_24,_2_28}-{x86_64,aarch64,ppc64le,s390x}
+  cibuildwheel
   build-wheels-pip
   delocate-macos-wheels
 deps =
@@ -245,44 +245,17 @@ commands =
   twine check --strict {env:PEP517_OUT_DIR}/*
 
 
-[testenv:build-dists-manylinux{1,2010,2014,_2_24,_2_28}-{x86_64,aarch64,ppc64le,s390x}]
-allowlist_externals =
-  {env:DOCKER_EXECUTABLE:docker}
-basepython = python3
+[testenv:cibuildwheel]
 description =
-  Build manylinux wheels in a container and put them into the dists/ folder
+  Build publishable wheel dists using `cibuildwheel` and
+  put them into the dists/ folder
 commands =
-  # NOTE: `-t` shouldn't be used here because GitHub Actions
-  # NOTE: workflows don't have TTY
-  {env:DOCKER_EXECUTABLE:docker} run \
-    -i --rm \
-    -v {toxinidir}:/io \
-    -e ANSIBLE_PYLIBSSH_CYTHON_TRACING \
-    ghcr.io/ansible/pylibssh-manylinux{env:MANYLINUX_VERSION_TAG}_{env:MANYLINUX_ARCH_TAG}:libssh-v{env:LIBSSH_VERSION:0.9.6} \
-    /io/build-scripts/build-manylinux-wheels.sh \
-    "manylinux{env:MANYLINUX_VERSION_TAG}_{env:MANYLINUX_ARCH_TAG}" \
-    {posargs:}
+  {envpython} -Im cibuildwheel {posargs}
 deps =
-isolated_build = true
-passenv =
-  # alternatively set `DOCKER_EXECUTABLE=podman` outside the container
-  DOCKER_EXECUTABLE
-  HOME
-  LIBSSH_VERSION
-setenv =
-  {[testenv]setenv}
-
-  x86_64: MANYLINUX_ARCH_TAG = x86_64
-  aarch64: MANYLINUX_ARCH_TAG = aarch64
-  ppc64le: MANYLINUX_ARCH_TAG = ppc64le
-  s390x: MANYLINUX_ARCH_TAG = s390x
-
-  manylinux1: MANYLINUX_VERSION_TAG = 1
-  manylinux2010: MANYLINUX_VERSION_TAG = 2010
-  manylinux2014: MANYLINUX_VERSION_TAG = 2014
-  manylinux_2_24: MANYLINUX_VERSION_TAG = _2_24
-  manylinux_2_28: MANYLINUX_VERSION_TAG = _2_28
-skip_install = true
+  cibuildwheel
+package = skip
+set_env =
+  CIBW_CONFIG_SETTINGS = with-cython-tracing={env:ANSIBLE_PYLIBSSH_CYTHON_TRACING:true}
 
 
 [testenv:lint]