Abstract: Frequency conversion, particularly tripling of coherent radiation of high intensity laser beams in the red or infrared (approximately 1.06 micrometers), is obtained at high efficiencies by operating a nonlinear optical element, such as a nonlinear crystal, at an efficiency of conversion to a first frequency that results in optimal input to the same or another nonlinear optical element for efficient conversion to a second frequency over a wide range of input beam intensities. An input beam from a Nd:glass laser operating at about 1.06 micrometers can be converted to a high quality output beam of triple the frequency, about 0.35 micrometers, with an overall conversion efficiency in excess of 75%.