There is no fast track immigration for temporary visitors. Waiting times vary depending on how many jumbos just landed ahead of you. It is a crapshoot.

You can expect the queues to get worse on November 20, as Japan introduces mandatory fingerprinting for almost all non-Japanese citizens:
http://www.stippy.com/japan-news-and...fingerprinted/

IMHO, it's inevitable that this new measure will cause us all more pain when entering NRT. But perhaps they'll respond to complaints with some measures to make things better. I guess it's possible that they would create elite lines - and that will mean fewer gates for the lumpen coachatariat. (When the temporary visitor lines got bad last year, I think, they responded to complaints by shifting staff from the Japanese citizens & residents lines).

On the way out of Japan, NH (and some other star alliance carriers) offer fast-track security for F passengers. The only time I had this rare privilege, I didn't bother with it - The security lines are not usually a big deal.