“On short notice” vs “At short notice”

I have heard both, and probably use both myself undistinguishly. My usual sources conflict on that one, actually. The New Oxford American Dictionary, which is, well, American, says:

at short (or a moment’s) notice
with little warning or time for preparation: tours may be canceled at short notice.

On the other hand, Merriam-Webster’s says

  • (US) We can be ready on short notice. = (Brit) We can be ready at short notice.
  • (US) Thank you for meeting with me on such short notice. = (Brit) Thank you for meeting with me at such short notice.

The Corpus of Contemporary American English agrees with the latter, as it gives 33 hits for “at short notice” against 187 hits for “on short notice”. Google ngrams gives the same picture, but slightly less contrasted:

British English ngram
American English ngram