Abstract: A reamer for precision machining of holes includes a reamer body and a knife plate supported above the exterior of the body and extending along the exterior. The knife plate has a front lower radial height cutting region and a rear taller radial height cutting region joined by an inclined step so that the first front region does the major cutting and the second rearward region does the finer machining. The front cutting region has an entrance bevel. The inclined flank shapes of the cutting regions are disclosed. Reamer guide strips supported along the support have a similarly shaped bevel and step as the knife plate.