Selective laser melting is a powder-based, additive-manufacturing process where a threedimensional part is produced, layer by layer, by using a high-energy laser beam to fuse the metallic powder particles. A particular challenge in this process is the selection of appropriate process parameters that result in parts with desired properties. In this study, we describe an approach to selecting parameters for high density (>99%) parts using 316L stainless steel. Though there has been significant success in achieving near-full density for 316L parts, this work has been limited to laser powers <225W. We discuss how we can exploit prior knowledge, design of computational experiments using a simple model of laser melting, and single-track experiments to determine the process parameters for use at laser powers up to 400W. Our results show that, at higher power values, there is a large range of scan speeds over which the relative density remains >99%, with the density reducing rapidly at high speeds due to insufficient melting, and less rapidly at low speeds due to the effect of voids created as the process enters keyhole mode.