We compare the performance of very fast simulated quenching; generalized simulated quenching, which unifies classical Boltzmann simulated quenching and Cauchy fast simulated quenching; and variable step size simulated quenching. The comparison is carried out by applying these algorithms to the design of diffractive optical elements for beam shaping of monochromatic, spatially incoherent light to a tightly focused image spot, whose central lobe should be smaller than the geometrical-optics limit. For generalized simulated quenching we choose values of visiting and acceptance shape parameters recommended by other investigators and use both a one-dimensional and a multidimensional Tsallis random number generator. We find that, under our test conditions, variable step size simulated quenching, which generates each parameter's new states based on the acceptance ratio instead of a certain theoretical probability distribution, produces the best results. Finally, we demonstrate experimentally a tightly focused image spot, with a central lobe 0.22-0.68 times the geometrical-optics limit and a relative sidelobe intensity 55%-60% that of the central maximum intensity. © 2008 Optical Society of America.