In this paper, a new, ray-tracing optimization for the design of secondary reflectors of linear Fresnel collectors is presented. Optimization is capable to produce the optimum shape of reflectors, by tailoring properly oriented segments, so that the maximum concentration of off-target rays is redirected back to the cylindrical receiver. As an illustrative example, it is applied to the design of the secondary reflector for an existing installation. The shapes of the secondary reflectors are different for the different vertical distances from the receiver. The optical performance of the various configurations is investigated by utilizing free, open source ray-tracing software. The maximum value of successful rays ratio, i.e. the fraction of sun rays that intersect the receiver, reaches 0.97 and 0.84, for secondary reflectors located 5 and 12.5 cm above the receiver, respectively. (C) 2019 Elsevier Ltd. All rights reserved.