Typical limitations of integrated antennas such as bidirectional radiation, power loss via substrate modes, and broad radiation patterns can be corrected using a substrate lens. In this paper, various slot-fed substrate lens antenna (SLA) configurations are examined, and a novel hybrid physical optics analysis technique, suitable for electrically small geometries, is presented. Based on this method, directivity and reflection loss calculations for elliptical and hyperhemispherical synthesized lenses are carried out. It is found that the conditions for maximum directivity and minimum reflection loss do not coincide, and thus certain performance compromises are necessary. The results are confirmed experimentally.