The Monte Carlo generalized rejection technique provides a continuous passage from the inverse equation sampling method to the uniform sampling rejection method; it is well known that the nonuniform rejection method can be used to achieve very significant increases in sampling efficiency. We have applied the nonuniform rejection method to the Klein-Nishina Probability Density Function and have obtained improved efficiencies over the uniform sampling method of up to 100% at high gamma-ray energies and 10 to 60% improved efficiencies in the energy range from 0.3 to 1.5 MeV, respectively.