Suzie, I for one appreciate the fact that you asked the question. I have contacted IOC on one ocassion asking them to pass to ATC that we request minimium track miles as a result of burning in excess of the fuel plan .... way in excess. The profile I was looking for was FL 130 over Sierra and 40 odd track miles .... and I am happy to say we got it. Granted this is often the profile before 7 am but we were arriving later in the day. What I was attempting to prevent by such a request was FL 130 and 120 track miles which I have had on a number of occasions.
The previous comments by some re the declaration of a fuel emergency is not a standard phrase and , if the situation requires such a declaration then it is important that it is not misunderstood. There is a reticence in our circles to use the term MAYDAY ( 30 mins remaining) however, in my case, performing a glide approach would raise the dry cleaning bill.