diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 4bc29c8207..c8b033e8a4 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -328,9 +328,6 @@ jobs:
           - arrangement: monolith
             database: Postgres
 
-          - arrangement: workers
-            database: Postgres
-
     steps:
       - name: Run actions/checkout@v2 for synapse
         uses: actions/checkout@v2
@@ -346,6 +343,30 @@ jobs:
         shell: bash
         name: Run Complement Tests
 
+  # XXX When complement with workers is stable, move this back into the standard
+  #     "complement" matrix above.
+  #
+  # See https://github.com/matrix-org/synapse/issues/13161
+  complement-workers:
+    if: "${{ !failure() && !cancelled() }}"
+    needs: linting-done
+    runs-on: ubuntu-latest
+
+    steps:
+      - name: Run actions/checkout@v2 for synapse
+        uses: actions/checkout@v2
+        with:
+          path: synapse
+
+      - name: Prepare Complement's Prerequisites
+        run: synapse/.ci/scripts/setup_complement_prerequisites.sh
+
+      - run: |
+          set -o pipefail
+          POSTGRES=1 WORKERS=1 COMPLEMENT_DIR=`pwd`/complement synapse/scripts-dev/complement.sh -json 2>&1 | gotestfmt
+        shell: bash
+        name: Run Complement Tests
+
   # a job which marks all the other jobs as complete, thus allowing PRs to be merged.
   tests-done:
     if: ${{ always() }}
diff --git a/changelog.d/13266.misc b/changelog.d/13266.misc
new file mode 100644
index 0000000000..d583acb81b
--- /dev/null
+++ b/changelog.d/13266.misc
@@ -0,0 +1 @@
+Do not fail build if complement with workers fails.