Clamping means in the form of an internal clamping means for fixing workpieces, in particular for the purpose of rotary machining of the said workpieces, having the following steps: a. the clamping means has a housing which extends in the axial direction, and b. the housing has a clamping cone which tapers towards a distal end and is oriented in the axial direction, and c. the clamping means has a clamping segment ring with a plurality of clamping segments which can be moved with respect to one another in the radial direction, and, d. on the outer side thereof, the clamping segments have a clamping face for bearing against the workpiece, and, e. on the inner side thereof, the clamping segments have an obliquely positioned sliding face for bearing against the clamping cone, with the result that the clamping segments can be moved radially with respect to one another by way of common axial movement with respect to the clamping cone, and f. the clamping means has at least one ejector pin which is received in an aperture of the housing and can be moved in the axial direction with respect to the housing, in order, as a result, to load the clamping segment ring with a force for separation from the clamping cone, characterized by the additional feature: g. a contact region for receiving or bearing against a distal end of the ejector pin is provided on a proximal end side of at least one clamping segment, and h. the contact region and the distal end of the ejector pin are configured in such a way that, in the case of the arrangement of the distal end of the ejector pin in the contact region, the ejector pin delimits a movability of the clamping segment in the radial direction to the outside in a positively locking way. a. the clamping means has a housing which extends in the axial direction, and b. the housing has a clamping cone which tapers towards a distal end and is oriented in the axial direction, and c. the clamping means has a clamping segment ring with a plurality of clamping segments which can be moved with respect to one another in the radial direction, and, d. on the outer side thereof, the clamping segments have a clamping face for bearing against the workpiece, and, e. on the inner side thereof, the clamping segments have an obliquely positioned sliding face for bearing against the clamping cone, with the result that the clamping segments can be moved radially with respect to one another by way of common axial movement with respect to the clamping cone, and f. the clamping means has at least one ejector pin which is received in an aperture of the housing and can be moved in the axial direction with respect to the housing, in order, as a result, to load the clamping segment ring with a force for separation from the clamping cone, characterized by the additional feature: g. a contact region for receiving or bearing against a distal end of the ejector pin is provided on a proximal end side of at least one clamping segment, and h. the contact region and the distal end of the ejector pin are configured in such a way that, in the case of the arrangement of the distal end of the ejector pin in the contact region, the ejector pin delimits a movability of the clamping segment in the radial direction to the outside in a positively locking way.