A method for the computer-assisted manufacture of a tooth replacement part or a dental auxiliary element by means of a machining tool, - wherein the tooth replacement part or the auxiliary element is machined from a blank by means of at least one tool of the machining tool, - wherein the blank is clamped in the machining tool so as to be rotatable about an axis of rotation which extends perpendicular to a feed axis of the at least one tool, - wherein a three-dimensional blank data set corresponding to the blank and comprising the axis of rotation is stored, - wherein a three-dimensional model data set of the tooth replacement part to be manufactured or of the dental auxiliary element to be manufactured is stored, - wherein the model data set has a first region having a first insertion axis and a second region having a second insertion axis, - wherein the first insertion axis and the second insertion axis are oriented in a skewed manner with respect to one another, - wherein the model data set is arranged in the blank data set in at least two positioning steps (S1, S2) and a result is made available to the machining tool as a position data set, - wherein the machining tool machines the tooth replacement part or the dental auxiliary element from the blank according to the position data set, characterised in that - in the first positioning step the first insertion axis of the model data set is oriented perpendicular to the axis of rotation of the blank data set, - in the second positioning step following the first positioning step the second insertion axis of the model data set is oriented perpendicular to the axis of rotation of the blank data set by a rotation of the model data set about the first insertion axis. - wherein the tooth replacement part or the auxiliary element is machined from a blank by means of at least one tool of the machining tool, - wherein the blank is clamped in the machining tool so as to be rotatable about an axis of rotation which extends perpendicular to a feed axis of the at least one tool, - wherein a three-dimensional blank data set corresponding to the blank and comprising the axis of rotation is stored, - wherein a three-dimensional model data set of the tooth replacement part to be manufactured or of the dental auxiliary element to be manufactured is stored, - wherein the model data set has a first region having a first insertion axis and a second region having a second insertion axis, - wherein the first insertion axis and the second insertion axis are oriented in a skewed manner with respect to one another, - wherein the model data set is arranged in the blank data set in at least two positioning steps (S1, S2) and a result is made available to the machining tool as a position data set, - wherein the machining tool machines the tooth replacement part or the dental auxiliary element from the blank according to the position data set, - in the first positioning step the first insertion axis of the model data set is oriented perpendicular to the axis of rotation of the blank data set, - in the second positioning step following the first positioning step the second insertion axis of the model data set is oriented perpendicular to the axis of rotation of the blank data set by a rotation of the model data set about the first insertion axis.