diff --git a/.cirrus.yml b/.cirrus.yml
deleted file mode 100644
index e805dd620b..0000000000
--- a/.cirrus.yml
+++ /dev/null
@@ -1,72 +0,0 @@
-env:
-  ### cirrus config
-  CIRRUS_CLONE_DEPTH: 1
-  ### compiler options
-  HOST:
-  WRAPPER_CMD:
-  # Specific warnings can be disabled with -Wno-error=foo.
-  # -pedantic-errors is not equivalent to -Werror=pedantic and thus not implied by -Werror according to the GCC manual.
-  WERROR_CFLAGS: -Werror -pedantic-errors
-  MAKEFLAGS: -j4
-  BUILD: check
-  ### secp256k1 config
-  ECMULTWINDOW: auto
-  ECMULTGENPRECISION: auto
-  ASM: no
-  WIDEMUL: auto
-  WITH_VALGRIND: yes
-  EXTRAFLAGS:
-  ### secp256k1 modules
-  EXPERIMENTAL: no
-  ECDH: no
-  RECOVERY: no
-  SCHNORRSIG: no
-  ELLSWIFT: no
-  ### test options
-  SECP256K1_TEST_ITERS:
-  BENCH: yes
-  SECP256K1_BENCH_ITERS: 2
-  CTIMETESTS: yes
-  # Compile and run the tests
-  EXAMPLES: yes
-
-# https://cirrus-ci.org/pricing/#compute-credits
-credits_snippet: &CREDITS
-  # Don't use any credits for now.
-  use_compute_credits: false
-
-cat_logs_snippet: &CAT_LOGS
-  always:
-    cat_tests_log_script:
-      - cat tests.log || true
-    cat_noverify_tests_log_script:
-      - cat noverify_tests.log || true
-    cat_exhaustive_tests_log_script:
-      - cat exhaustive_tests.log || true
-    cat_ctime_tests_log_script:
-      - cat ctime_tests.log || true
-    cat_bench_log_script:
-      - cat bench.log || true
-    cat_config_log_script:
-      - cat config.log || true
-    cat_test_env_script:
-      - cat test_env.log || true
-    cat_ci_env_script:
-      - env
-
-linux_container_snippet: &LINUX_CONTAINER
-  container:
-    dockerfile: ci/linux-debian.Dockerfile
-    # Reduce number of CPUs to be able to do more builds in parallel.
-    cpu: 1
-    # Gives us more CPUs for free if they're available.
-    greedy: true
-    # More than enough for our scripts.
-    memory: 2G
-
-task:
-  name: "C++ (public headers)"
-  << : *LINUX_CONTAINER
-  test_script:
-    - g++ -Werror include/*.h
-    - clang -Werror -x c++-header include/*.h
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index eb3009a5df..a372d3d944 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -768,6 +768,24 @@ jobs:
         run: env
         if: ${{ always() }}
 
+  cxx_headers_debian:
+    name: "C++ (public headers)"
+    runs-on: ubuntu-latest
+    needs: docker_cache
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v3
+
+      - name: CI script
+        uses: ./.github/actions/run-in-docker-action
+        with:
+          dockerfile: ./ci/linux-debian.Dockerfile
+          tag: linux-debian-image
+          command: >
+            g++ -Werror include/*.h &&
+            clang -Werror -x c++-header include/*.h
+
   sage:
     name: "SageMath prover"
     runs-on: ubuntu-latest