A simple method is proposed to significantly enhance the broadside directivity of a simple slot antenna over a wide bandwidth. This improvement is achieved by introducing a simple optimised dielectric superstructure with an axial variation of permittivity. In this antenna, both the superstructure and ground plane are cylindrical in shape with an area of 1.62(0)(2). The antenna has a measured peak directivity of 18.1 dBi and an extremely wide 3 dB directivity bandwidth of 51.1%. A WR-75 waveguide is used to feed the slot antenna. The antenna is well matched over the entire directivity bandwidth, which extends from 8.75 to 14.75 GHz. The measured average aperture efficiency is approximate to 88% over the 3 dB directivity bandwidth.