Some airlines have unpublished criteria for who they'll comp and who they won't. If you have a regular travel agent or corporate travel coordinator, ask him/her to arrange the comp through his/her airline sales rep. They have more leverage than you do. Makes it smoother.

To the degree that AA is an option, their agents will usually try to talk you into the Challenge - a fast track to status based on flights during a 90-day period. (More details in the AA forum.) It beats the standard qualification process but isn't as good as a comp. I'd call back at least three times for a comp before signing up for the Challenge. If you complete a Challenge this time of year, your status will be good through the March 2004-Feb. 2005 program year. You'll have calendar 2004 to requalify on your own.

I'd check out the three airlines' Forums to see what their frequent flyers think of them, too - not just in terms of their FF programs, but relative to the overall experience.