I am now a firm believer that the "Braves Model" is the one to follow. Not too long ago, I was firmly against locking up any player who was still under team control. Why pay big bucks for them when you still have them under control for relatively little?
Since free agent contracts have skyrocketed to beyond sane levels, I think it's almost a must to lock these guys up early.
If it were up to me, I'd lock up Mayer, Abreu, and Narvaez as well. It doesn't have to be this year, and it doesn't have to be as large a contract as Anthony's, but I'd extend them before they get to free agency. It's always a risk, but one well worth taking, IMO.