An adjustment device for adjusting the position of at least one cutter of a fine machining tool, particularly a reamer, with respect to a cutter support (ST) is described. To allow the cutter to be adjusted as precisely as possible, the cutter support (ST) borders at least one pressure chamber (DK) which is arranged in the adjustment direction of the cutter (S) with a displacement with respect to it and which is filled with a pressure medium which can be placed under pressure using a pressure generation device. Between the cutter (S) and the pressure chamber (DK), a cutter support wall (W) remains which is elastically deformable upon application of pressure by the pressure transfer means to adjust the cutter position.