We use nonimaging, statistical-ray optics and ray-tracing simulations to study external light traps as a cost-effective means to enhance the absorption of optically imperfect solar cells. Our main finding is that the optical performance of a cell may be compromised substantially without affecting its overall performance if a trap is being used. As a result, simpler cell construction that gives better charge-transport abilities may be considered. As a case study, we show that the thickness of a silicon cell may be reduced to less than a micron without compromising its efficiency and that the efficiency of perovskite cell may increase substantially, almost up to its theoretical limit.