Most large solar concentrators designed for high flux concentration;at high collection efficiency are based on imaging primary mirrors and nonimaging secondary concentrators. In this paper, we offer an alternative purely imaging two-stage solar concentrator that can attain high flux concentration at high collection efficiency. Possible practical virtues include: (1) an inherent large gap between absorber and secondary mirror; (2) a restricted angular range on the absorber; and (3) an upward-facing receiver where collected energy can be extracted via the (shaded) apex of the parabola. We use efficiency-concentration plots to characterize the solar concentrators considered, and to evaluate the potential improvements with secondary concentrators.