Step-wound package of tape

A package of tape including a plurality of body portions. Each body portion is formed as a series of steps, each step including a plurality of turns of tape that are wrapped about a core. During formation of each step, the winding position of the tape is varied. In one embodiment, the winding position of the tape is oscillated a fraction of the width of the tape per revolution of the core, or during a revolution of the core. In an alternative embodiment, the winding position of the tape is varied by a fraction of the width of the tape in a first direction after each approximately full turn of tape. During formation of an immediately adjacent step in the same body portion, the winding position of the tape is varied by a fraction of the width of the tape in a second direction, opposite the first direction.