We demonstrate a stack of two III-nitride laser diodes (LDs) interconnected by a tunnel junction grown by plasma-assisted molecular beam epitaxy. Hydrogen-free growth is used to obtain as-grown p-type conductivity essential for buried tunnel junctions (TJ). We show the impact of the design of tunnel junction. In particular, we show that, apart from the beneficial piezoelectric polarization inside the TJ, heavy doping reduces the differential resistivity even further. The device starts to lase at a wavelength of 459 nm with a slope efficiency (SE) of 0.7 W/A followed by lasing at 456 nm from the second active region doubling the total SE to 1.4 W/A. This demonstration opens new possibilities for the fabrication of stacks of ultraviolet and visible high power pulsed III-nitride LD.