We discuss the engineering of p-AlGaN cladding layers for achieving efficient tunnel-injected III-Nitride ultraviolet light emitting diodes (UV LEDs) in the UV-A spectral range. We show that the capacitance-voltage measurements can be used to estimate the compensation and doping in the p-AlGaN layers located between the multi-quantum well region and the tunnel junction layer. By increasing the p-type doping concentration to overcome the background compensation, on-wafer external quantum efficiency and wall-plug efficiency of 3.37% and 1.62%, respectively, were achieved for the tunnel-injected UV LEDs emitting at 325 nm. We also show that interband tunneling hole injection can be used to realize UV LEDs without any acceptor doping. The work discussed here provides new understanding of hole doping and transport in AlGaN-based UV LEDs and demonstrates the excellent performance of tunnel-injected LEDs for the UV-A wavelength range. Published by AIP Publishing.