A bullet that will retain markings from a firearm barrel when fired from such firearm. The bullet comprises a right cylindrical core with opposed ends, one such opposed end having a tapered section integrally connected thereto. The core is formed from a lead-free composition of a polymer and filler and selectively retains its integrity when fired from the firearm or is frangible. The right cylindrical core has a jacket that is cylindrical and formed from a thermoplastic polymer or copper. The thermoplastic polymer has a softening point above firearm barrel temperatures.