A sub-caliber bullet with an aerodynamic shape has long-range accuracy due to a high muzzle velocity and reduced time of flight to a target. The bullet has a forward portion, a mid-portion and an aft portion. The forward portion has a density in excess of 10/cm3 while the mid-portion has a lower density. The bullet has an aspect ratio of at least 5:1 and a diameter, d, that satisfies a Power Law equation: d=D*(x/L)n where D is a maximum bullet diameter, L is the length, x is a distance rearward from a nose of the bullet and n is a Power Law exponent that is between 0.5 and 0.75. In some embodiments, a blind bore extends into the mid-portion from the aft portion and a sustainer propellant within the blind bore ignites as the bullet exits a gun muzzle to provide a velocity boost and to overcome aerodynamic drag.