A parabolic reflector for an antenna has a plurality of concentric annular sections arranged in series from a first annular section nearest a central axis of the reflector to a last annular section defining an outer perimeter of the reflector. Each section has a parabolic reflecting surface between inner and outer perimeters. The sections are configured such that the focal point associated with at least the last section lies inside an internal volume of the reflector and are arranged with respect to each other along the central axis, such that an overall depth of the reflector is substantially minimized. The inner perimeters of all the sections are preferably arranged to lie substantially on a plane which is perpendicular to the central axis. The outer perimeter of each section except the last section is preferably connected with the inner perimeter of the succeeding section by means of an annular strip. The strips may either each have an angle of inclination to the reflector central axis of between 0° and 3° or they may lie on respective cones running from the respective inner perimeters of the respective sections to which they are joined, to the furthest located focal point or ring.