Embodiments of the invention relate to a reamer for machining a workpiece by chip removal. Embodiments of the reamer can incorporate a holder, having a receiving opening disposed on a workpiece-side end face and having an internal thread, a holder bore extending inside the holder in a longitudinal direction thereof and opening into the receiving opening, an exchangeable head, having a cutting-nose element having a plurality of cutting noses disposed in a distributed manner in a circumferential direction, an exchangeable-head shank having an external thread corresponding to the internal thread disposed in the receiving opening, a bearing contact element disposed between the cutting-nose element and the exchangeable-head shank and having a first bearing contact surface for bearing contact on a first support surface disposed on the workpiece-side end face, with an exchangeable-head bore corresponding to the holder bore extends through the exchangeable head in a longitudinal direction thereof.