Material costs may be reduced and electrical properties improved by utilizing thinner solar cells. Light trapping makes it possible to reduce wafer thickness without compromising optical absorption in a silicon solar cell. In this work we present a comprehensive comparison of the light-trapping properties of various bi-periodic structures with a square lattice. The geometries that we have investigated are cylinders, cones, inverted pyramids, dimples (half-spheres), and three more advanced structures, which we have called the roof mosaic, rose, and zigzag structure. Through simulations performed with a 20 μm thick Si cell, we have optimized the geometry of each structure for light trapping, investigated the performance at oblique angles of incidence, and computed efficiencies for the different diffraction orders for the optimized structures. We find that the lattice periods that give optimal light trapping are comparable for all structures, but that the light-trapping ability varies considerably between the structures. A far-field analysis reveals that the superior light-trapping structures exhibit a lower symmetry in their diffraction patterns. The best result is obtained for the zigzag structure with a simulated photo-generated current Jph of 37.3 mA/cm2, a light-trapping efficiency comparable to that of Lambertian light-trapping.