In a method of rolling tubes in a stretch-reducing rolling mill having a group drive in which the elongation, and therefore the tension is increased by increasing the speed of an auxiliary drive motor relative to that of a main drive motor, the length of the trailing "thickened end", which must be rejected as scrap, is reduced by increasing the elongation from the point in time at which the start of the trailing end portion of the tube reaches the last stand. This trailing end portion is that portion which receives a larger wall thickness than the central portion of the tube as a result of the reduced tension exerted in the trailing end portion of prior art practices. The start of this trailing end portion can be predicted from experience or by rolling a sample tube without subjecting its trailing end portion to the said increased elongation and measuring the wall thickness at the trailing end portion of the sample tube.