In photon transport calculations by a Monte Carlo method, the solution of the inverse Klein-Nishina cumulative distribution function for random selection of a photon energy upon Compton scattering is not practical; moreover, Koblinger's procedure cannot be applied for incoming photon energies less than . In this case the sampling rejection methods (SRMs), especially the nonuniform ones, represent a good alternative. A number of SRMs for the Klein-Nishina probability density function are presented; some of the methods have very high selection efficiencies. These techniques are tested within the bounds of computer time required for a successful selection. At least one of them is appreciably advantageous over those previously proposed.