An improved adapter sleeve is submitted which has a shank for insertion into a toolholder for a machine tool, wherein a tool socket for holding a tool is formed in the shank, wherein a number of slots are disposed along the shank so that the shank can be compressed during clamping, wherein a cutting head is formed which is arranged on a front side (F) of the shank. In one embodiment, the cutting head has an insert seat for a cutting insert.