A method is given for the design of a class of wide-angle reflectors in which the aberrations are reduced by coating the reflector surface with a dielectric. At microwave frequencies this dielectric may take the form of an array of metal plates or waveguides and the constraint imposed by this form greatly simplifies the analysis. The path of the feed point is chosen so that only selected rays from it are equally phased. It is then found that both of the reflector's profiles and the path of the feed point can be described by a single parameter. The residual aberrations of several cylindrical systems, including the corrected parabola and circle, are analysed to find a reflector for which the scanning arc is the circle with centre at the vertex of the reflector. A refocusing procedure, which is found to be necessary, produces this scanning arc. Experimental results in agreement with the theory are given.It is shown that the design principle can be used to programme a step-wise procedure for the design of corrected surfaces using nonconstrained natural dielectric coatings.