The spillover noise of a reflector antenna can be reduced by attaching a shroud extending forward from the edge of the reflector; the shroud prevents ground radiation from entering the feed. Symmetrical paraboloidal antennas of diameter 40 wavelengths, equipped with cylindrical and conical shrouds, are analyzed using the method of moments. A cylindrical shroud, parallel to the reflector axis, may reduce antenna noise, but it raises the sidelobe level in the front hemisphere substantially and can also reduce antenna gain. These drawbacks can be overcome by using a conical shroud, flared outward. Such a shroud reduces the spillover lobes in the back hemisphere, thus lowering the antenna noise temperature, but generates a conical sidelobe in the front hemisphere. The peak level of this sidelobe can be reduced by building the shroud using two cones of different flare angles or by curving its cross section. The decrease in noise temperature, as well as the location and level of the conical sidelobes in the front hemisphere, can be predicted to useful accuracy using geometrical optics. The addition of a shroud increases the level of cross polarization near the main beam. However, this effect is reduced if the sharp corner where the shroud joins the reflector rim is replaced by a smooth transition. The level of cross polarization is then at a level comparable to that produced by scattering from feed-support struts.