How to delete a chatter post file attachment via the Chatter REST API?

[robguttman]

We're using the Chatter REST API to attach files to records (as feed-items).  This works well.

I also seem to be able to delete these chatter posts (feed-items) using the Chatter REST API - i.e., I see that the post is removed from the record in both the Chatter area as well as the "Notes & Attachments" area.

However, the actual file still seems to live in Salesforce and occupy file storage space - no good.  I can see the "orphaned" files in the Chatter > Files section where I can manually delete them but of course I want the Chatter REST API to be able to delete them.

I've tried deleting the attachment directly using the files service but I get 404s when I do this.  (I'm grabbing the attachment downloadUrl field and converting it into a delete request - so the url should be dead on.)

So how can I delete these files via the Chatter REST API so that they no longer consume file storage space?

Thanks.
- Rob