Advances in Photovoltaic technology using multijunction cells allow sunlight-to-electrical energy conversion efficiencies of 25 percent with the potential of reaching 30 percent. The main drawback with these cells is their high cost. By using a concentrating Photovoltaic (CPV) solar collector, the area/cost of the cells relative to the total system area/cost can be reduced substantially. The design of CPV systems has one constraint not found in standard thermal solar concentrators, namely the target is square and the irradiance uniformity goal is very tight. A novel two-stage solar collector system designed for the National Renewable Energy Laboratory (NREL) is presented here. By tailoring the radial profile of the primary mirror that is slightly non-parabolic and using a straight square tube secondary, designs for concentrations between 100-2,000 suns can achieve uniformity under 3 percent and greater than 95 percent efficiencies. A design using a non-rotationally symmetric primary design is also presented, which reduces the problems with shading by spiders that attach the secondary to the primary mirror.