Electrons impinging on a target can release secondary electrons and/or they can be scattered out of the target. It is well established that the number of escaping electrons per primary electron depends on the target composition and dimensions, the energy, and incidence angle of the primary electrons, but there are suggestions that the target's shape and surface roughness also influence the secondary emission. We present a further modification of the model of secondary electron emission from dust grains which is applied to non-spherical grains and grains with defined surface roughness. It is shown that the non-spherical grains give rise to a larger secondary electron yield, whereas the surface roughness leads to a decrease in the yield. Moreover, these effects can be distinguished: the shape effect is prominent for high primary energies, whereas the surface roughness predominantly affects the yield at the low-energy range. The calculations use the Lunar Highlands Type NU-LHT-2M simulant as a grain material and the results are compared with previously published laboratory and in situ measurements.