diff --git a/ci/build.linux.gitlab-ci.yml b/ci/build.linux.gitlab-ci.yml
index 1c1fa022b..3713a5826 100644
--- a/ci/build.linux.gitlab-ci.yml
+++ b/ci/build.linux.gitlab-ci.yml
@@ -106,6 +106,8 @@ build:linux:doc:
     EIGEN_CI_C_COMPILER: clang
     EIGEN_CI_CXX_COMPILER: clang++
     EIGEN_CI_BEFORE_SCRIPT: ". ci/scripts/build_and_install_doxygen.sh Release_1_13_2"
+  rules:
+    - if: $CI_PIPELINE_SOURCE == "push" && $CI_PROJECT_NAMESPACE == "libeigen"
 
 # # Sanitizers (Disabled because ASAN hangs and MSAN requires instrumented libc++)
 # build:linux:cross:x86-64:clang-12:default:asan:
diff --git a/ci/deploy.gitlab-ci.yml b/ci/deploy.gitlab-ci.yml
index 0784fcb9b..311313920 100644
--- a/ci/deploy.gitlab-ci.yml
+++ b/ci/deploy.gitlab-ci.yml
@@ -12,11 +12,11 @@ deploy:tag:nightly:
     - linux
     - eigen-runner
   rules:
-    - if: $CI_PIPELINE_SOURCE == "schedule" && $CI_PROJECT_NAMESPACE == "libeigen"
-    - if: $CI_PIPELINE_SOURCE == "web" && $CI_PROJECT_NAMESPACE == "libeigen"
+    - if: $CI_PIPELINE_SOURCE == "schedule" && $CI_PROJECT_NAMESPACE == "libeigen" && $CI_COMMIT_BRANCH == $CI_DEFAULT_BRANCH
+    - if: $CI_PIPELINE_SOURCE == "web" && $CI_PROJECT_NAMESPACE == "libeigen" && $CI_COMMIT_BRANCH == $CI_DEFAULT_BRANCH
 
 # Upload docs if pipeline succeeded.
-deploy:doc:nightly:
+deploy:docs:
   stage: deploy
   image: busybox
   dependencies: [ build:linux:doc ]
@@ -27,6 +27,7 @@ deploy:doc:nightly:
     - mv ${EIGEN_CI_BUILDDIR}/doc/html public
   pages:
     path_prefix: $PAGES_PREFIX
+    expire_in: never
   artifacts:
     name: "$CI_JOB_NAME_SLUG-$CI_COMMIT_REF_SLUG"
     paths:
@@ -37,3 +38,6 @@ deploy:doc:nightly:
   rules:
     - if: $CI_PIPELINE_SOURCE == "schedule" && $CI_PROJECT_NAMESPACE == "libeigen"
     - if: $CI_PIPELINE_SOURCE == "web" && $CI_PROJECT_NAMESPACE == "libeigen"
+    - if: $CI_PIPELINE_SOURCE == "push" && $CI_PROJECT_NAMESPACE == "libeigen"
+      variables:
+        PAGES_PREFIX: docs-$CI_COMMIT_REF_NAME