Abstract: A medical tissue-abrading instrument, for instance a shaver, includes an instrument handpiece at which manipulators for actuating an abrasion means, for instance a cutting or grinding head, are arranged and in which a fluid passage adjustable in cross-section by means of a valve is formed for sucking off abraded tissue and/or for supplying scavenging fluid. The valve is a manually operable slider valve. The valve piston of the valve includes a control edge having an edge shape which causes a change of the passage cross-section at a particular ratio, preferably linearly, during continuous actuation of the valve.