This paper presents a novel broadband, low-profile dielectric resonator antenna using relatively low dielectric constant substrate material. The rectangular DRA is fed with a stepped microstrip feed to ensure efficient coupling. Bandwidths in excess of 17% are obtained. In addition, the paper investigates methods to miniaturize the antenna using metallic strips or patches. Substantial size reduction is demonstrated while maintaining a reasonable bandwidth. Simulations as well as experimental results are presented.