To perform deburring in an economical, but reliable way, based on a purpose for which a tool and a device, and an available method are provided.

A rotationally driven tool for deburring bore holes which join laterally into a cylindrical recess 14 is disclosed. The tool contains a cutting head seated on a shaft, wherein the cutting head contains at least one cutting edge, which extends in the axial direction at least in some sections. In order to perform the deburring process reliably and with as little effort as possible, the tool contains at least one inner flow-enhancing agent channel 24, from which at least one cutoff channel extends, which joins in the area of the cutting head in an outer circumferential surface thereof preferably at a circumferential distance at least to the one cutting edge. Because the diameter of the cutting head is selected such that it can be introduced into the recess with a radial play, the feeding of the pressurized flow-enhancing agent leads to a radial excursion of the tool shaft.