With Twitter OAuth, the user gets the following:
I only need to post tweets, is it possible to only ask for only that?
Facebook supports a "scope" parameter when requesting authentication, but I don't see anything like that for Twitter: Twitter Authorization
I don't think that is possible at the moment. The only permissions available at the app settings page are "Read only", "Read and Write" (which you're using) and "Read, Write and Access direct messages".