Two-dimensional numerical simulation is employed to assess a number of possible design approaches aimed at optimizing the internal quantum efficiency of BeZnO-based light-emitting diodes grown along the c-axis. First, we describe the material parameters and the numerical simulation methods used to study these devices. Second, the effects of thickness, doping, and alloy composition of the BeZnO electron blocking layer are analysed in order to maximise the carrier confinement in the active region. The optimum number of quantum wells and barrier doping level are also addressed, as well as the effects of the buffer layer thickness. Finally, the limitations on the device performance imposed by the nonuniform lateral current distribution are discussed.