Really, when you brake, you have better breaking if you don't engage the clutch until your getting pretty slow.
In the winter, engine braking is the only way to go done decent size hill up here. Just leave it in first, and coast all the way down, and right at the bottom where there is a slight flat spot, put your brakes on.
Also, in extreme emergencys, I have heard of people having total brake failure on a road course and coming from a full straight to a hard right. They did a slight brake tap in the middle of the turn to see if they were there and they just fell to the floor. He just started down shifting and reved the hell out of the car, way over red line. Quickly he started to slow down and had enough to avoid the wall at the end of the run off.