diff --git a/.github/workflows/push.yml b/.github/workflows/push.yml
index 35fd4a766bb..0c4f1badb70 100644
--- a/.github/workflows/push.yml
+++ b/.github/workflows/push.yml
@@ -1,6 +1,12 @@
 name: Core
 
-on: [push]
+on:
+  push:
+    branches-ignore:
+      - master
+      - MOODLE_[0-9]+_STABLE
+    tags-ignore:
+      - v[0-9]+.[0-9]+.[0-9]+*
 
 env:
   php: 7.4
diff --git a/.travis.yml b/.travis.yml
index 0c565f37901..6d52469b5d7 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -19,6 +19,12 @@ services:
 addons:
   postgresql: "9.6"
 
+branches:
+  except:
+    - master
+    - /MOODLE_[0-9]+_STABLE/
+    - /^v[0-9]+\.[0-9]+\.[0-9]+.*/
+
 jobs:
     # Enable fast finish.
     # This will fail the build if a single job fails (except those in allow_failures).