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A novel solid-state laser-pumping scheme is proposed that combines a reflective lamp chamber and a compound parabolic concentrator (CPC) as a light guide. The CPC is made of a transparent material of high refractive index, and light is guided by the total internal reflection, with drastically reduced reflection losses. Material is chosen so that the absorption losses are minimized in the pumping wavelength range. The lamp chamber is designed with the principles of nonimaging optics, which ensures that the radiation is efficiently transferred from the lamp to the input aperture of the CPC. The pumping efficiency was first estimated theoretically, which gave us enough justification for the more accurate calculations with ray tracing. Single as well as multiple pumping cavities are discussed. New pumping geometry results in significantly increased pumping efficiency compared with conventional geometries. Also the lamp and the laser rod are separated, leading to reduced thermal load. We found that the proposed pumping method is also applicable to diode-pumped lasers.