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Planar Fresnel zone plates (FZP) substitute the curved surfaces of a Fresnel reflector for an stepped one, getting advantages concerning to manufacturing and prize. Besides, this technology provides the possibility of designing conformed beam antennas, as for example when a double beam is required. The main disadvantage of FZP is the inherent loss in gain of the stepped approximation, though, as we have been able to prove, efficiency results to be very reasonable and equilibrated with the other advantages for many uses. Conic Fresnel Zone Plates (CFZP) consist of FZPs developed over a conic surface instead of a planar one. This change provides more efficiency preserving the advantages of FZPs without a noticeable increase in size or occupancy. The synthesis procedure of CFZPs drives to a new conception of reflector that we have called Fresnel flat zone cone (FFZC) whose structure is very simple in comparison with FZPs and CFZPs, while the degree of approximation and, then, the performance is much better. A procedure for optimal synthesis of FFZCs is also presented.