An overend unwind system (10) for unwinding tacky elastomeric fiber threads (12) such as uncoated spandex thread, capturing the ballooning affect of the thread (12) as the thread (12) leaves the spool (22), applying a first-stage tension control on the thread adjacent where the thread leaves the spool (22), feeding the unwound thread (12) to a nip (14) in a downstream process, and applying a final tension increment to the thread (12) adjacent where the thread (12) enters the downstream process. All thread guide surfaces (66, 70, 88) encountered by the thread (12) after leaving the spool (22), and while the thread (12) is under designed operating tension, are moving surfaces, such that the tensioned thread (12) thereby experiences a reduced level of drag as the thread (12) traverses its path of travel from the spool (22) to the downstream process.