AlGaN-based deep-ultraviolet light-emitting diode (LED) structures, which radiate light at 305 and 290 nm, have been grown on sapphire substrates using an AlN epilayer template. The fabricated devices have a circular geometry to enhance current spreading and light extraction. Circular UV LEDs of different sizes have been characterized. It was found that smaller disk LEDs had higher saturation optical power densities but lower optical powers than the larger devices. This trade-off between power and power density is a result of a compromise between electrical and thermal resistance, as well as the current crowding effect (which is due to the low electrical conductivity of high aluminum composition n- and p-AlGaN layers). Disk UV LEDs should thus have a moderate size to best utilize both total optical power and power density. For 0.85 mm × 0.85 mm interdigitated LEDs, a saturation optical power of 2.9 mW (1.8 mW) at 305 nm (290 nm) was also obtained under dc operation.