Additive manufacturing provides a number of benefits in terms of infinite freedom to design complex parts and reduced lead-times while globally reducing the size of supply chains as it brings all production processes under one roof. However, additive manufacturing (AM) lags far behind conventional manufacturing in terms of surface quality. This proves a hindrance for many companies considering investment in AM. The aim of this work is to investigate the effect of varying process parameters on the resultant roughness of the down-facing surfaces in selective laser melting (SLM). A systematic experimental study was carried out and the effects of the interaction of the different parameters and their effect on the surface roughness (Sa) were analyzed. It was found that the interaction and interdependency between parameters were of greatest significance to the obtainable surface roughness, though their effects vary greatly depending on the applied levels. This behavior was mainly attributed to the difference in energy absorbed by the powder. Predictive process models for optimization of process parameters for minimizing the obtained Sa in 45° and 35° down-facing surface, individually, were achieved with average error percentages of 5% and 6.3%, respectively, however further investigation is still warranted.