Dielectric stepped-index flat lens antennas for operation at 12 GHz are presented. A brick-shaped dielectric with a permittivity profile optimized for focusing is sandwiched between the metallic plates of an open-ended parallel-plate waveguide. A tapered slot antenna is placed at the focal point of the dielectric lens, thereby creating antennas with high directivity of 16.8 and 15.8 dBi, respectively. In the two versions of the antenna, the parallel-plate waveguide operates in TEM-mode and in the first higher-order TE-mode, respectively. The dielectric profile is realized by appropriate mixtures of alumina ceramic powder and microscopic hollow glass spheres, realizing permittivity ranging from εrel = 1.31 to εrel = 3.24. The design of the complete antennas is based on geometrical optics followed by optimizations with a full-wave electromagnetic solver. Measurements show good agreement with simulations.