A banding machine applies bands about objects for packaging, decorative, or other purposes. An object is banded with tape by: grasping a starting end of a tape extending from a tape roll between a first roller and a brake, with the first roller being situated adjacent the object alongside a second roller; orbiting the object with tape roll to apply the tape to the circumference of the object; during the orbit, pressing the starting end of the tape against the object with a wiper, and releasing the tape starting end from the brake; upon the tape's orbital approach of the tape starting end, receiving the tape over the first and second rollers; extending a knife between the first and second rollers to cut the tape, thereby defining a finishing end of the tape extending about the object; and pressing the finishing end of the tape against the object with a wiper.