diff --git a/.travis.yml b/.travis.yml
index d933ccce06..a72e81552f 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,127 +1,82 @@
-sudo: required
+---
+# vi: ts=2 sw=2 et:
+
+language: bash
 dist: bionic
 services:
-    - docker
+  - docker
 
 env:
-    global:
-        - AUTHOR_EMAIL="$(git log -1 $TRAVIS_COMMIT --pretty=\"%aE\")"
-        - CI_MANAGERS="$TRAVIS_BUILD_DIR/travis-ci/managers"
-        - CI_TOOLS="$TRAVIS_BUILD_DIR/travis-ci/tools"
-        - REPO_ROOT="$TRAVIS_BUILD_DIR"
+  global:
+    - AUTHOR_EMAIL="$(git log -1 $TRAVIS_COMMIT --pretty=\"%aE\")"
+    - CI_MANAGERS="$TRAVIS_BUILD_DIR/travis-ci/managers"
+    - CI_TOOLS="$TRAVIS_BUILD_DIR/travis-ci/tools"
+    - REPO_ROOT="$TRAVIS_BUILD_DIR"
+  jobs:
+    - DEBIAN_RELEASE=testing PHASE="RUN_GCC"
+    - DEBIAN_RELEASE=testing PHASE="RUN_GCC_ASAN_UBSAN"
+    - DEBIAN_RELEASE=testing PHASE="RUN_CLANG"
+    - DEBIAN_RELEASE=testing PHASE="RUN_CLANG_ASAN_UBSAN"
 
 stages:
-    - name: Build & test
-      if: type != cron
+  # 'Test' is the default stage (for matrix jobs)
+  - name: Test
+    if: type != cron
 
     # Run Coverity periodically instead of for each commit/PR
-    - name: Coverity
-      if: type = cron
+  - name: Coverity
+    if: type = cron
 
+# Matrix job definition - this is run for each combination of env variables
+# from the env.jobs array above
+before_install:
+  - sudo apt-get -y -o Dpkg::Options::="--force-confnew" install docker-ce
+  - docker --version
+install:
+  - $CI_MANAGERS/debian.sh SETUP
+script:
+  - $CI_MANAGERS/debian.sh $PHASE || travis_terminate 1
+after_script:
+  - $CI_MANAGERS/debian.sh CLEANUP
+
+# Inject another (single) job into the matrix for Coverity
 jobs:
-    include:
-        - stage: Build & test
-          name: Debian Testing
-          language: bash
-          env:
-              - DEBIAN_RELEASE="testing"
-              - CONT_NAME="systemd-debian-$DEBIAN_RELEASE"
-              - DOCKER_EXEC="docker exec -ti $CONT_NAME"
-          before_install:
-              - sudo apt-get -y -o Dpkg::Options::="--force-confnew" install docker-ce
-              - docker --version
-          install:
-              - $CI_MANAGERS/debian.sh SETUP
-          script:
-              - $CI_MANAGERS/debian.sh RUN || travis_terminate 1
-          after_script:
-              - $CI_MANAGERS/debian.sh CLEANUP
+  include:
+    - stage: Coverity
+      language: bash
+      env:
+        - FEDORA_RELEASE="latest"
+        - TOOL_BASE="/var/tmp/coverity-scan-analysis"
+        - DOCKER_RUN="docker run -v $TOOL_BASE:$TOOL_BASE:rw --env-file .cov-env"
+          # Coverity env variables
+        - PLATFORM="$(uname)"
+        - TOOL_ARCHIVE="/var/tmp/cov-analysis-$PLATFORM.tgz"
+        - SCAN_URL="https://scan.coverity.com"
+        - UPLOAD_URL="https://scan.coverity.com/builds"
+        - COVERITY_SCAN_PROJECT_NAME="$TRAVIS_REPO_SLUG"
+        - COVERITY_SCAN_NOTIFICATION_EMAIL="${AUTHOR_EMAIL}"
+        - COVERITY_SCAN_BRANCH_PATTERN="$TRAVIS_BRANCH"
+          # Encrypted COVERITY_SCAN_TOKEN env variable
+          # Generated using `travis encrypt -r systemd/systemd COVERITY_SCAN_TOKEN=xxxx`
+        - secure: "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"
+      before_install:
+        - sudo apt-get -y -o Dpkg::Options::="--force-confnew" install docker-ce
+        - docker --version
+      install:
+        # Install Coverity on the host
+        - $CI_TOOLS/get-coverity.sh
+          # Export necessary env variables for Coverity
+        - env | grep -E "TRAVIS|COV|TOOL|URL" > .cov-env
+          # Pull a Docker image and start a new container
+        - $CI_MANAGERS/fedora.sh SETUP
+      script:
+        - set -e
+          # Preconfigure with meson to prevent Coverity from capturing meson metadata
+        - $DOCKER_EXEC meson cov-build -Dman=false
+          # Run Coverity
+        - $DOCKER_EXEC tools/coverity.sh build
+        - $DOCKER_EXEC tools/coverity.sh upload
 
-        - name: Debian Testing (ASan+UBSan)
-          language: bash
-          env:
-              - DEBIAN_RELEASE="testing"
-              - CONT_NAME="systemd-debian-$DEBIAN_RELEASE"
-              - DOCKER_EXEC="docker exec -ti $CONT_NAME"
-          before_install:
-              - sudo apt-get -y -o Dpkg::Options::="--force-confnew" install docker-ce
-              - docker --version
-          install:
-              - $CI_MANAGERS/debian.sh SETUP
-          script:
-              - $CI_MANAGERS/debian.sh RUN_ASAN || travis_terminate 1
-          after_script:
-              - $CI_MANAGERS/debian.sh CLEANUP
-
-        - name: Debian Testing (clang)
-          language: bash
-          env:
-              - DEBIAN_RELEASE="testing"
-              - CONT_NAME="systemd-debian-$DEBIAN_RELEASE"
-              - DOCKER_EXEC="docker exec -ti $CONT_NAME"
-          before_install:
-              - sudo apt-get -y -o Dpkg::Options::="--force-confnew" install docker-ce
-              - docker --version
-          install:
-              - $CI_MANAGERS/debian.sh SETUP
-          script:
-              - $CI_MANAGERS/debian.sh RUN_CLANG || travis-travis_terminate 1
-          after_script:
-              - $CI_MANAGERS/debian.sh CLEANUP
-
-        - name: Debian Testing (clang ASan+UBSan)
-          language: bash
-          env:
-              - DEBIAN_RELEASE="testing"
-              - CONT_NAME="systemd-debian-$DEBIAN_RELEASE"
-              - DOCKER_EXEC="docker exec -ti $CONT_NAME"
-          before_install:
-              - sudo apt-get -y -o Dpkg::Options::="--force-confnew" install docker-ce
-              - docker --version
-          install:
-              - $CI_MANAGERS/debian.sh SETUP
-          script:
-              - $CI_MANAGERS/debian.sh RUN_CLANG_ASAN || travis_terminate 1
-          after_script:
-              - $CI_MANAGERS/debian.sh CLEANUP
-
-        - stage: Coverity
-          language: bash
-          env:
-              - FEDORA_RELEASE="latest"
-              - CONT_NAME="coverity-fedora-$FEDORA_RELEASE"
-              - DOCKER_EXEC="docker exec -ti $CONT_NAME"
-              - TOOL_BASE="/var/tmp/coverity-scan-analysis"
-              - DOCKER_RUN="docker run -v $TOOL_BASE:$TOOL_BASE:rw --env-file .cov-env"
-              # Coverity env variables
-              - PLATFORM="$(uname)"
-              - TOOL_ARCHIVE="/var/tmp/cov-analysis-$PLATFORM.tgz"
-              - SCAN_URL="https://scan.coverity.com"
-              - UPLOAD_URL="https://scan.coverity.com/builds"
-              - COVERITY_SCAN_PROJECT_NAME="$TRAVIS_REPO_SLUG"
-              - COVERITY_SCAN_NOTIFICATION_EMAIL="${AUTHOR_EMAIL}"
-              - COVERITY_SCAN_BRANCH_PATTERN="$TRAVIS_BRANCH"
-              # Encrypted COVERITY_SCAN_TOKEN env variable
-              # Generated using `travis encrypt -r systemd/systemd COVERITY_SCAN_TOKEN=xxxx`
-              - secure: "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"
-          before_install:
-              - sudo apt-get -y -o Dpkg::Options::="--force-confnew" install docker-ce
-              - docker --version
-          install:
-              # Install Coverity on the host
-              - $CI_TOOLS/get-coverity.sh
-              # Export necessary env variables for Coverity
-              - env | grep -E "TRAVIS|COV|TOOL|URL" > .cov-env
-              # Pull a Docker image and start a new container
-              - $CI_MANAGERS/fedora.sh SETUP
-          script:
-              - set -e
-              # Preconfigure with meson to prevent Coverity from capturing meson metadata
-              - $DOCKER_EXEC meson cov-build -Dman=false
-              # Run Coverity
-              - $DOCKER_EXEC tools/coverity.sh build
-              - $DOCKER_EXEC tools/coverity.sh upload
-
-              - set +e
-          after_script:
-              - $CI_MANAGERS/fedora.sh CLEANUP
+        - set +e
+      after_script:
+        - $CI_MANAGERS/fedora.sh CLEANUP
diff --git a/travis-ci/managers/debian.sh b/travis-ci/managers/debian.sh
index 60f6237606..a2a987d8fd 100755
--- a/travis-ci/managers/debian.sh
+++ b/travis-ci/managers/debian.sh
@@ -9,23 +9,25 @@
 # export CONT_NAME="my-fancy-container"
 # travis-ci/managers/debian.sh SETUP RUN CLEANUP
 
-PHASES=(${@:-SETUP RUN RUN_ASAN CLEANUP})
+PHASES=(${@:-SETUP RUN RUN_ASAN_UBSAN CLEANUP})
 DEBIAN_RELEASE="${DEBIAN_RELEASE:-testing}"
-CONT_NAME="${CONT_NAME:-debian-$DEBIAN_RELEASE-$RANDOM}"
+CONT_NAME="${CONT_NAME:-systemd-debian-$DEBIAN_RELEASE}"
 DOCKER_EXEC="${DOCKER_EXEC:-docker exec -it $CONT_NAME}"
 DOCKER_RUN="${DOCKER_RUN:-docker run}"
 REPO_ROOT="${REPO_ROOT:-$PWD}"
-ADDITIONAL_DEPS=(python3-libevdev
-                 python3-pyparsing
-                 clang
-                 perl
-                 libpwquality-dev
-                 fdisk
-                 libfdisk-dev
-                 libp11-kit-dev
-                 libssl-dev
-                 libzstd-dev
-                 zstd)
+ADDITIONAL_DEPS=(
+    clang
+    fdisk
+    libfdisk-dev
+    libp11-kit-dev
+    libpwquality-dev
+    libssl-dev
+    libzstd-dev
+    perl
+    python3-libevdev
+    python3-pyparsing
+    zstd
+)
 
 function info() {
     echo -e "\033[33;1m$1\033[0m"
@@ -54,7 +56,7 @@ for phase in "${PHASES[@]}"; do
             $DOCKER_EXEC apt-get -y build-dep systemd
             $DOCKER_EXEC apt-get -y install "${ADDITIONAL_DEPS[@]}"
             ;;
-        RUN|RUN_CLANG)
+        RUN|RUN_GCC|RUN_CLANG)
             if [[ "$phase" = "RUN_CLANG" ]]; then
                 ENV_VARS="-e CC=clang -e CXX=clang++"
             fi
@@ -62,8 +64,8 @@ for phase in "${PHASES[@]}"; do
             $DOCKER_EXEC ninja -v -C build
             docker exec -e "TRAVIS=$TRAVIS" -it $CONT_NAME ninja -C build test
             ;;
-        RUN_ASAN|RUN_CLANG_ASAN)
-            if [[ "$phase" = "RUN_CLANG_ASAN" ]]; then
+        RUN_ASAN_UBSAN|RUN_GCC_ASAN_UBSAN|RUN_CLANG_ASAN_UBSAN)
+            if [[ "$phase" = "RUN_CLANG_ASAN_UBSAN" ]]; then
                 ENV_VARS="-e CC=clang -e CXX=clang++"
                 # Build fuzzer regression tests only with clang (for now),
                 # see: https://github.com/systemd/systemd/pull/15886#issuecomment-632689604
diff --git a/travis-ci/managers/fedora.sh b/travis-ci/managers/fedora.sh
index b3c85ebd09..cc665021d4 100755
--- a/travis-ci/managers/fedora.sh
+++ b/travis-ci/managers/fedora.sh
@@ -9,38 +9,32 @@
 # export CONT_NAME="my-fancy-container"
 # travis-ci/managers/fedora.sh SETUP RUN CLEANUP
 
-PHASES=(${@:-SETUP RUN RUN_ASAN CLEANUP})
+PHASES=(${@:-SETUP RUN RUN_ASAN_UBSAN CLEANUP})
 FEDORA_RELEASE="${FEDORA_RELEASE:-rawhide}"
-CONT_NAME="${CONT_NAME:-fedora-$FEDORA_RELEASE-$RANDOM}"
+CONT_NAME="${CONT_NAME:-systemd-fedora-$FEDORA_RELEASE}"
 DOCKER_EXEC="${DOCKER_EXEC:-docker exec -it $CONT_NAME}"
 DOCKER_RUN="${DOCKER_RUN:-docker run}"
 REPO_ROOT="${REPO_ROOT:-$PWD}"
-ADDITIONAL_DEPS=(dnf-plugins-core
-                 jq iputils
-                 hostname libasan
-                 python3-pyparsing
-                 python3-evdev
-                 libubsan
-                 clang
-                 llvm
-                 perl
-                 libfdisk-devel
-                 libpwquality-devel
-                 openssl-devel
-                 p11-kit-devel)
+ADDITIONAL_DEPS=(
+    clang
+    dnf-plugins-core
+    hostname libasan
+    jq iputils
+    libfdisk-devel
+    libpwquality-devel
+    libubsan
+    llvm
+    openssl-devel
+    p11-kit-devel
+    perl
+    python3-evdev
+    python3-pyparsing
+)
 
 info() {
     echo -e "\033[33;1m$1\033[0m"
 }
 
-error() {
-    echo >&2 -e "\033[31;1m$1\033[0m"
-}
-
-success() {
-    echo >&2 -e "\033[32;1m$1\033[0m"
-}
-
 # Simple wrapper which retries given command up to five times
 _retry() {
     local EC=1
@@ -94,8 +88,8 @@ for phase in "${PHASES[@]}"; do
             $DOCKER_EXEC ninja -v -C build
             $DOCKER_EXEC ninja -C build test
             ;;
-        RUN_ASAN|RUN_CLANG_ASAN)
-            if [[ "$phase" = "RUN_CLANG_ASAN" ]]; then
+        RUN_ASAN|RUN_GCC_ASAN_UBSAN|RUN_CLANG_ASAN_UBSAN)
+            if [[ "$phase" = "RUN_CLANG_ASAN_UBSAN" ]]; then
                 ENV_VARS="-e CC=clang -e CXX=clang++"
                 MESON_ARGS="-Db_lundef=false" # See https://github.com/mesonbuild/meson/issues/764
             fi
@@ -110,46 +104,6 @@ for phase in "${PHASES[@]}"; do
                 -t $CONT_NAME \
                 meson test --timeout-multiplier=3 -C ./build/ --print-errorlogs
             ;;
-        RUN_BUILD_CHECK_GCC|RUN_BUILD_CHECK_CLANG)
-            ARGS=(
-                "--optimization=0"
-                "--optimization=2"
-                "--optimization=3"
-                "--optimization=s"
-                "-Db_lto=true"
-                "-Db_ndebug=true"
-            )
-
-            if [[ "$phase" = "RUN_BUILD_CHECK_CLANG" ]]; then
-                ENV_VARS="-e CC=clang -e CXX=clang++"
-                $DOCKER_EXEC clang --version
-            else
-                $DOCKER_EXEC gcc --version
-            fi
-
-            for args in "${ARGS[@]}"; do
-                SECONDS=0
-                info "Checking build with $args"
-                # Redirect meson/ninja logs into separate files, otherwise we
-                # would trip over Travis' log size limit
-                if ! docker exec $ENV_VARS -it $CONT_NAME meson --werror $args build &> meson.log; then
-                    cat meson.log
-                    error "meson failed with $args"
-                    exit 1
-                fi
-
-                if ! $DOCKER_EXEC ninja -v -C build &> ninja.log; then
-                    cat ninja.log
-                    error "ninja failed with $args"
-                    exit 1
-                fi
-
-                $DOCKER_EXEC rm -fr build
-                rm -f meson.log ninja.log
-                success "Build with $args passed in $SECONDS seconds"
-            done
-
-            ;;
         CLEANUP)
             info "Cleanup phase"
             docker stop $CONT_NAME