For H1B visas there certainly was an expedited process - a couple of times our firm paid ~$1000 to get the response within 2 weeks, rather than 'several months'. Reducing uncertainty was valuable to us, since otherwise we might have been mentoring an excellent employee who could be plucked out of the workplace by the INS on any random day : and due to the whole bureaucracy thing, any 'appeal' would be a huge, huge waste of time (and life).