A possible way to concentrate sun light is by using a Fresnel reflector: a large number of small mirrors (called heliostats) that mimic the behavior of a large concentrator, replacing it. These heliostats can move to track the sun, keeping its light concentrated onto the receiver. Fresnel concentrators, however, may have important losses. If the heliostats are spaced from each other, some light will miss them and be lost. If the heliostats are close to each other, they will block part of each other's reflected light, also producing losses. One possible way to minimize these losses is to intersect two focusing Fresnel concentrators forming a Compact Linear Fresnel Reflector - CLFR. Although improving on a simple focusing Fresnel concentrator, these optics are still not optimal. Here new geometries for Fresnel reflectors are explored, minimizing their losses and increasing their concentration. This is achieved by changing the overall shape of the primary, making it a wave-shaped trough surface and/or by allowing for a variable size and shape of the heliostats as a function of the position in the heliostat field. These new Fresnel concentrators may also be combined with secondaries significantly improving their total concentration, which now approaches the theoretical maximum. (C) 2009 Elsevier Ltd. All rights reserved.