A fixing device for fixing a boring bar on a material-removing machine includes a reducing sleeve with a hollow profile arranged on a front face which faces away from a machine chuck. The boring bar is received in an interior of the hollow profile. An end region of the boring bar projects from the hollow profile and carries a cutting tool. The hollow profile has a wall arranged between the interior and an exterior of the hollow profile. The wall has a first thickness and a second thickness. The first thickness is less than the second thickness. The first thickness is established at a side of the fixing device where the cutting tool projects radially from the boring bar. A longitudinal axis of the hollow profile is parallel to and at a distance from the axis of the reducing sleeve which is coaxial with the interior of the boring bar.