A bullet with controlled fragmentation has a core in the form of a generally cylindrical body having a forward end and a rear end and intermediate side portions extending there between, the forward end of the core defining a cavity, a jacket encompassing the rear end and at least selected portions of the sides of the core, the jacket having a sidewall having a first drive band portion having a first wall thickness, and a second portion immediately forward of the drive band portion having a second thickness less than the first thickness, the exterior of the jacket defining a cannelure groove encircling the bullet, and the cannelure groove being positioned forward of the first drive band portion. The drive band may have forward edge defining a step. The bullet of the present invention may also be received in the case mouth of a rimless case and be partially protruding therefrom.