In a steady rest (1) for centring a rotationally symmetrical workpiece (2) in the space, consisting of: two housing halves (4, 5) arranged at a distance from one another and firmly connected together, a middle steady rest arm (6) arranged between the two housing shells (4, 5) that is mounted in the housing shells (4, 5) by means of an actuation piston (7) so as to be moved in an axial direction (3) towards the workpiece (2), and two outer steady rest arms (11, 12) that are in a driving connection with the middle steady rest arm (6) by means of a guide slide (13) which has a control track (14) on two opposite outside sides, on which a roller (16) attached to the free ends (15) of both outer steady rests (11, 12) is arranged which roll along the control track (14), workpieces (2) with different diameters should be held in the space. This is achieved in that the particular control track (14) of the guide slide (13) has at least two control sections (21, 22, 25) and that at least two rollers (16) spaced apart from one another are provided on the particular outer steady rest arm (11, 12), which are in an active contact with one each of the control sections (21, 22, 25) depending on the position of the guide slide (13) in the housing shells (4, 5).