Quantum-dot systems are confined semiconductor structures which exhibit a fully discrete spectrum due to the size confinement in all directions. The position of the energy levels inside such structures can be changed by adjusting their geometrical dimensions. Such structures are particularly interesting for optical applications for two reasons: (i) both the electrons and holes are confined in the same small physical region, and therefore the strength of recombination processes is increased, and (ii) by changing the position of the energy levels, one can in principle tune quantum-dot lasers over a wide range of wavelengths. The presence of size confinement gives rise to two competing effects: on one hand it causes an upward shift of the energy levels, and on the other it enhances the Coulomb attraction between electrons and holes. These effects tend to shift the position of the exciton energies in opposite directions, so that a careful modelling of such structures is required in order to understand which is the dominant effect and how the excitons behave as a function of confinement. While there have been several studies on ideal systems, we attempt to model a system more closely aligned to experiment. In this study we investigate: (i) the effect of the shape of the lateral potential of a quantum disk, i.e. parabolic and hard-wall; (ii) the effect of wave-function leakage in the barries; and (iii) the effect of the light-heavy hole mixing on the effective masses.