Light trapping by means of external cavities theoretically offers the same potential to improve the efficiency of solar converters as does concentration. The ideal efficiency of 86% could be reached by any combination of concentration and light trapping, provided all the etendue of the cell is coupled either to itself (giving light trapping) or to the sun (giving concentration). But with real solar cells, there are optimum conditions of concentration and light trapping which maximize the efficiency. The possibility of achieving these conditions is compared between two optical systems: (1) axisymmetric Fresnel lens with plane upper surface, and ellipsoidal cavity, (2) similar Fresnel lens plus secondary lens using total internal reflections to trap light. With regard to a deep-emitter cell, of moderate technology, either system can attain near optimum conditions, giving an efficiency about 4% points above 1-sun efficiency. With a more speculative cell model assuming back mirroring and cell thinning to reduce series resistance, the maximum efficiency (predicted 8% points above 1-sun efficiency) cannot be obtained due to limitations of the optical system, and about 5% points above 1-sun efficiency appears feasible.