A toothed workpiece having a modified surface geometry may be produced by a diagonal generating method by means of a modified tool whose surface geometry comprises a modification. The modification may be described by a linear and/or quadratic function, with the coefficients of this linear and/or quadratic function. Pitch and/or crowning of the modification may vary in dependence on the angle of rotation of the tool and/or on the tool width position. The specific modification of the tool produces a corresponding modification on the surface of the workpiece by the diagonal generating method, with a desired modification of the surface geometry of the workpiece being specified and a modification of the surface geometry of the tool suitable for producing this desired modification being determined in combination with a diagonal ratio of the diagonal generating method suitable for producing the desired modification.