The introduction of twist during the spinning of carbon nanotubes from their arrays (forests) has been widely applied in making ultrastrong, stiff, and lightweight nanotube fibers. Here, for the first time, an important observation of a double-peak behavior of the tensile properties, as a function of the twist angle, that is different from the single peak of traditional fibers is reported. Raman spectra show that the new peak arises from the collapse of nanotubes, showing a strong "nano" element in applying the ancient draw-and-twist technique, besides the downsizing. A qualitative continuum model is also presented to describe the collapse-induced enhancement as well as traditional fibers. Our combined experimental and theoretical studies indicate the direction of full utilization of the nano element in improving the mechanical properties of nanotube fibers.