Rewinder for producing paper logs, comprising a winding station with a first winding roller (R1), a second winding roller (R2) and a third winding roller (R3) driven by corresponding electric motors (M1, M2, M3), comprising a detection system capable to detect a succession of diameters (DE) of the log (L) being formed in the winding station and a programmable electronic unit (UE) connected to the electric motors. The system compares the measured diameters with a succession of corresponding diameters of predetermined value (DT) and to calculate a sequence of differences (e1, e2,..., en) between these values (DE, DT). The electronic unit determines a parameter (a) related to the trend over time of the values (e1, e2,..., en). The electronic unit changes the relative speed of the first and second roll depending on the value of the parameter (a).