A tool for machining a workpiece, having: - a cutting insert having at least one cutting edge, - a tool holder, which extends substantially along a holder longitudinal axis and has at a workpiece-side end a cutting insert receptacle for receiving the cutting insert, the cutting insert receptacle having an upper clamping finger and a lower clamping jaw, and wherein the tool holder comprises a first internal thread, - a substantially wedge-shaped clamping element, which is fastenable in the cutting insert receptacle for wedging the cutting insert in the tool holder, wherein the clamping element comprises on a top side a first bearing portion for bearing against the cutting insert, and on a bottom side lying opposite the top side a second bearing portion for bearing against the lower clamping jaw, wherein the first bearing portion extends substantially along a first bearing axis and the second bearing portion extends substantially along a second bearing axis, and wherein the clamping element comprises a through bore, and - a screw for fastening the clamping element in the cutting insert receptacle and for simultaneously wedging the cutting insert in the tool holder, wherein, in the mounted state of the tool, the clamping element is disposed between the cutting insert and the lower clamping jaw of the tool holder and the screw engages in the first internal thread through the through bore, characterized in that, in the mounted state of the tool, the first bearing axis runs transverse to the holder longitudinal axis, and the second bearing axis runs parallel to the holder longitudinal axis of the tool holder, and in that a longitudinal axis of the through bore runs parallel to the second bearing axis. - a cutting insert having at least one cutting edge, - a tool holder, which extends substantially along a holder longitudinal axis and has at a workpiece-side end a cutting insert receptacle for receiving the cutting insert, the cutting insert receptacle having an upper clamping finger and a lower clamping jaw, and wherein the tool holder comprises a first internal thread, - a substantially wedge-shaped clamping element, which is fastenable in the cutting insert receptacle for wedging the cutting insert in the tool holder, wherein the clamping element comprises on a top side a first bearing portion for bearing against the cutting insert, and on a bottom side lying opposite the top side a second bearing portion for bearing against the lower clamping jaw, wherein the first bearing portion extends substantially along a first bearing axis and the second bearing portion extends substantially along a second bearing axis, and wherein the clamping element comprises a through bore, and - a screw for fastening the clamping element in the cutting insert receptacle and for simultaneously wedging the cutting insert in the tool holder, wherein, in the mounted state of the tool, the clamping element is disposed between the cutting insert and the lower clamping jaw of the tool holder and the screw engages in the first internal thread through the through bore, characterized in that, in the mounted state of the tool, the first bearing axis runs transverse to the holder longitudinal axis, and the second bearing axis runs parallel to the holder longitudinal axis of the tool holder, and in that a longitudinal axis of the through bore runs parallel to the second bearing axis.