How to delete files from Basecamp using their API?

I was able to successfully use the Basecamp File API to get the list of the files in a project, and download files. But how can I delete files? Issuing a DELETE instead of a GET on the file doesn't seem to do the trick for m开发者_如何学Pythone. Am I missing something?

It looks like they don't expose an REST API method for DELETEing files.