People use hevi-shot becuase it is heavier than lead. Since it is heavier, it has more down-range energy and since it has more down-rage energy, you can get by with a smaller shot size. A rough example would be that a hevi-shot shell that is using #6 shot will have the same energy as that of a lead #5. This is extremely nice because the #6 shot is smaller, resulting in more pellets in the shell. Examples of hevi-shot type shells are Hevi-Shot Hevi-13, Winchester Xtended Range HD, Remington Wingmaster HD, and Federal Heavyweight, just to name a few.