A stretch reducing rolling mill for rolling pipes has a plurality of roll stands arranged in series in a conveying direction of a pipe. A wall thickness measuring device determines a wall thickness progression of the pipe prior to rolling. A control unit controls respective rotational speeds of the roll stands. A pipe position measuring device is arranged in front of the roll stands and continuously measures a current longitudinal coordinate of the pipe. The measured values of the longitudinal coordinate of the pipe are transmitted to the control unit. The control unit controls the rotational speeds of the roll stands based on both the determined wall thickness progression and the transmitted measured values of the current longitudinal coordinate of the pipe, in order to compensate for wall thickness variations of the pipe. A stretch reducing rolling mill is designed to carry out the method.