A machine vise has incorporated into it a pair of collet jaws that allows for the machining of top surfaces and ends of a held part. The collet jaws are secured to each of the clamping blocks on the machine vise. The collet jaws include at least one collet pocket shaped into the inside surface of each collet jaw. The collet pockets are designed to receive collet pads which are shaped to hold a generally cylindrical part with varying diameters. By having more than one collet pocket within each collet jaw, several different sizes of collet pads can be utilized at the same time and a part with varying diameters can be held securely in place within the machine vise.