Abstract: A two honing process eliminates the need for subsequent brush honing at another location. The honing process which is accomplished with a single head uses rough honing stones or tools for the initial phase, and finishing tools of tightly compacted abrasive containing plastic monofilaments for the second phase. The phases may be contiguous, slightly spaced, or preferably overlap for up to about one-half of the rough honing phase. When the finishing honing tools are operating alone, the angle of movement of the tools is somewhat askew of the oil retaining ridges and grooves formed by the rough honing operation. With the process, the oil bearing surfaces have improvements in plateau finish and surface topography, avoid abrasive contamination caused by hard finishing tools, and obtain such improvements in a more economic manner.