--- a/taskcluster/ci/desktop-test/tests.yml
+++ b/taskcluster/ci/desktop-test/tests.yml
@@ -346,16 +346,18 @@ mochitest-webgl:
         chunked: true
         config:
             by-test-platform:
                 default:
                     - mozharness/configs/unittests/linux_unittest.py
                     - mozharness/configs/remove_executables.py
         extra-options:
             - --mochitest-suite=mochitest-gl
+    # Bug 1296733: llvmpipe with mesa 9.2.1 lacks thread safety
+    allow-software-gl-layers: false
 
 reftest:
     description: "Reftest run"
     suite: reftest/reftest
     treeherder-symbol: tc-R(R)
     chunks: 8
     mozharness:
         script: mozharness/scripts/desktop_unittest.py