The square cornet type nonimaging concentrator has been shown useful for moderate concentration of sunlight onto photovoltaic solar cells, since it creates no hot spots at the exit aperture. In this paper are presented the mathematical formulas on which the cornet designs are based, results from computer simulations on overall cornet performance compared with measurements as well as exit aperture intensity variations, measured optical concentration ratios under controlled circumstances, and cell temperature measurements under realistic circumstances. In an Appendix are given performance curves for a large number of cornets as determined from computer simulations, covering the useful range of concentration factors and acceptance angles.