Clamping holder for cutting inserts has a rigid holding part and a clamping finger elastically movable with respect to the rigid holding part that define opposite sides of a substantially U-shaped recess for receiving a cutting insert. One of these two sides has first and second spaced-apart contact points for one side of a cutting insert and the opposite side has a third contact point. A stop for limiting the insertion depth of the cutting inset into the recess is provided inside the recess. That side of the cutting insert that has the third contact point is additionally assigned the stop, which is configured such that it simultaneously acts as a further, fourth lateral contact point opposite the first and second contact points and as a stop for limiting the insertion depth of the cutting insert.