Abstract: The invention relates to a tool head, especially a fine drill head, comprising a machine shank and a tool shank having a joint center axis, wherein the tool shank has a rigid core and a head with a tool, supported by a parallel spring arrangement and is able to be elastically displaced in relation thereto, said head having several limbs which emanate therefrom and form the parallel spring arrangement, whereby at least one of said limbs is fixed to the core or machine shank. The inventive tool head also comprises a device for radial displacement of the head in relation to the core, comprising a positioning device which has a conical part and is guided inside the core. The conical part bears against a contact part of the parallel spring arrangement under pressure when in use. The core is configured with the parallel spring arrangement in a single piece.