One exemplary embodiment can be a process for improving a hydrotreated stream for lubricating a machine. The hydrotreated stream can include an effective amount of one or more saturated hydrocarbons. Generally, the process includes hydrogenating the hydrotreated stream having no more than about 300 ppm, by weight, sulfur based on the weight of the stream in a hydrogenation reaction zone to produce a product stream having no more than about 5 ppm, by weight, sulfur.