diff --git a/tests/test-zstd-versions.py b/tests/test-zstd-versions.py
index 4ee778fe5..a0a179ce6 100755
--- a/tests/test-zstd-versions.py
+++ b/tests/test-zstd-versions.py
@@ -205,7 +205,8 @@ if __name__ == '__main__':
     # Retrieve all release tags
     print('Retrieve all release tags :')
     os.chdir(clone_dir)
-    tags = get_git_tags() + [head]
+    alltags = get_git_tags() + [head]
+    tags = [t for t in alltags if t >= 'v0.4.0']
     print(tags)
 
     # Build all release zstd