Methods and apparatus for stretching a plastic tape before the tape is joined in proper registration to a web of material in a machine. The apparatus comprises: means for advancing a leading portion of a flexible tape along a tape pathway; a guide that guides a lagging portion of the tape; a brake mounted to the guide and activatable to clamp a portion of the lagging portion of the tape at a first location; a sensor mounted to the guide and arranged to output a characteristic signal whenever the passage of a boundary of a structural feature of a particular type, repeatedly formed on or attached to the tape, is detected at a second location upstream of the first location; and a controller for causing the leading portion of the tape to be advanced a predetermined distance at regular spaced intervals of time and for causing the brake to clamp the lagging portion in response to the output of the characteristic signal by the sensor. The second location is selected such that the brake clamps the lagging portion while the leading portion is still being advanced, whereby a portion of the tape disposed downstream from the brake is stretched.