Carryback of Net Operating Loss -- NY Minimum Tax and Fed taxes

I own a small C Corp; and it has been reporting small profits and paying the Minimum taxfor the past few years. In 2009, the Corporation has a small Net Operating Loss that I am thinking of carrying back to past years. But then I got to thinking that even if the carryback wipes out the profit, the Corp still have to pay the Minimum Tax in those years; and therefore would not get a refund.

Am I correct? Or the Coporation would get a refund of the Minimum tax that was paid in the last 2 years -- IF the NOL is carried back?

For Federal taxes, how do I get a refund for carryback for the regular

Thanks.