Abstract: The present invention relates to a method and a device in the chip-removing machining of a work-piece by means of a rotatable tool with a shaft arranged in a headstock. The tool is displaceable in an axial direction both towards and away from the work-piece, and in a plane substantially perpendicular to the arbor. Arranged around a machining point is an enclosure. The enclosure has a first opening that is designed to press against the work-piece around the point to be or being machined. A second opening in the enclosure is made in a wall substantially perpendicular to the shaft. This opening is designed, during machining, to press against a plane plate arranged behind the tool and around the headstock, substantially perpendicular to the arbor, so that during machining there is a substantially enclosed space in the area around the tool and the machining point. The device includes a line for delivering cutting fluid to the machining point.