Depends how amenable your QA people are. They'll have to write the BDD tests in a fairly rigid syntax, and you'll have to write the bindings, but we find that it works pretty well.

Because you're writing the bindings, you can turn the BDD "Given I am logged in; When I click Buy; Then my basket should contain 1 item" into whatever you want. I've been playing with testing against the controllers in ASP.NET MVC; you could make the bindings talk to your REST API instead. The project I'm working on tests against different tiers: we've got some that have bindings for testing against the database, some that test against an existing (end-to-end) COM API, and some that test against the viewmodel in the UI.