A powder-based projectile useful in the manufacture of gun ammunition comprising a jacket having an inner volume which is tapered from a maximum diameter adjacent the open end of the jacket to a minimum diameter adjacent the closed end of the jacket and a core formed outside the jacket and having a complementary tapered geometry with respect to the inner volume of the jacket. Projections from the outer surface of the core are embedded within the inner wall of the jacket to enhance the spin stability of the jacket/core combination and to enhance the frangibility of the projectile upon it striking a target. A method for the manufacture of the projectile is disclosed.