We propose a novel design method for reflective nonimaging concentrators that is based on maximizing system performance beyond standard nonimaging metrics of transfer efficiency and proscribed illumination distribution. This new technique enables system operation characteristics to influence the algorithm, including nongeometrical parameters. This algorithm is termed non-edge-ray design (NERD) because we found that edge rays do not always give optimal illumination design. The case of a diode-pumped, Nd:YAG solid state laser is provided as a confirmation of the design utility. The pump-to-mode configuration, which includes a nonimaging pump cavity reflector, is the focus of this investigation. The merit function of the design process includes not only the transfer efficiency from an extended, 2-D laser diode array, but also the mode coupling of the absorption distribution within a laser rod to its desired output mode. Standard edge-ray design is shown to limit performance, with both numerical and experimental results. Two alternative pump cavity reflectors are developed and the improvements in the outputs from the lasers in TEM00 modes are presented. A periodic cavity sees over 8% improvement in optical efficiency at an output power of 10 W, while an averaging cavity provides nearly 5% improvement.