diff --git a/.github/workflows/libclang-python-tests.yml b/.github/workflows/libclang-python-tests.yml
index 43ded0af3ac21..801a701724789 100644
--- a/.github/workflows/libclang-python-tests.yml
+++ b/.github/workflows/libclang-python-tests.yml
@@ -22,12 +22,6 @@ on:
       - '.github/workflows/libclang-python-tests.yml'
       - '.github/workflows/llvm-project-tests.yml'
 
-concurrency:
-  # Skip intermediate builds: always.
-  # Cancel intermediate builds: only if it is a pull request build.
-  group: ${{ github.workflow }}-${{ github.ref }}
-  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
-
 jobs:
   check-clang-python:
     # Build libclang and then run the libclang Python binding's unit tests.
diff --git a/.github/workflows/llvm-project-tests.yml b/.github/workflows/llvm-project-tests.yml
index 17a54be16badc..95a3890c0d2dc 100644
--- a/.github/workflows/llvm-project-tests.yml
+++ b/.github/workflows/llvm-project-tests.yml
@@ -51,7 +51,7 @@ concurrency:
   # Cancel intermediate builds: only if it is a pull request build.
   # If the group name here is the same as the group name in the workflow that includes
   # this one, then the action will try to wait on itself and get stuck.
-  group: llvm-project-${{ github.workflow }}-${{ inputs.projects }}${{ github.ref }}
+  group: llvm-project-${{ github.workflow }}-${{ inputs.projects }}-${{ inputs.python_version }}${{ github.ref }}
   cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
 
 jobs: