TYPO3 Backend Layout Control

I'm using TYPO3's backend layout feature on a multi site install. This meant that I was seeing every backend layout I'd set up on every page in every site, which isn't ideal. So how do you control which backend layouts are available? TSConfig of course!

TCEFORM.pages {
  # Storagepage of layouts
  backend_layout.PAGE_TSCONFIG_ID = 0
  backend_layout_next_level.PAGE_TSCONFIG_ID = 0
}

Obviously replace 0 with the PID of the page where the backend layout records are stored.