diff --git a/cibuildwheel/linux.py b/cibuildwheel/linux.py
index c230d8cf..8367705e 100644
--- a/cibuildwheel/linux.py
+++ b/cibuildwheel/linux.py
@@ -122,7 +122,7 @@ def build(options: BuildOptions) -> None:
                     log.build_start(config.identifier)
 
                     dependency_constraint_flags: List[PathOrStr] = []
-                    if config.identifier.startswith("pp"):
+                    if config.identifier.startswith("pp36"):
                         # Patch PyPy to make sure headers get installed into a venv
                         patch_path = resources_dir / "pypy_venv.patch"
                         patch_docker_path = PurePath("/pypy_venv.patch")