A movable fixture for milling rail heads of slide rails arranged in a track bed includes: a rotating milling head mounted in a milling head drive mechanism supported by a chassis. The milling head has at least one cutting tooth comprising several cutting plates for milling the rail heads and a disc-shaped tool carrier connected to the milling head drive mechanism. The tool carrier includes cassettes assembled with cutting plates arranged around their periphery. The cassettes are arranged in several carrier segments connected to the tool carrier so they can be detached. The cassettes are arranged peripherally on the tool carrier with at least two assembled cutting plates, the cassettes being different with regard to at least one of: a number of cutting teeth; distances of the cutting teeth from each other; rake angle of the individual cutting plates; or inclination angle of the individual cutting plates.