A bicone over a finite ground plane is designed that has on average 2.8 dB more gain over a 10:1 band than its free-space counterpart. Metrics are established that enable a better understanding of antenna performance taking into account both the impedance and the radiation pattern. The effects of a finite sized ground plane are explored. To improve antenna performance over electrically small ground plane, a recessed geometry is proposed and studied. A recessed ground plane and bicone configurations are found that have better performance than the free-space bicone over 70% of the 10:1 band. Theoretical results are well supported by the measurements.