Although individual carbon nanotubes (CNTs) are superior as constituents to polymer chains, the mechanical and thermal properties of CNT fibers (CNTFs) remain inferior to synthetic fibers due to the failure of embedding CNTs effectively in superstructures. Conventional techniques resulted in a mild improvement of target properties while achieving parity at best on others. Here, a Double-Drawing technique is developed to rearrange the constituent CNTs in both mesoscale and nanoscale morphology. Consequently, the mechanical and thermal properties of the resulting CNTFs can simultaneously reach their highest performances with specific strength ~3.30 N/tex, work of rupture ~70 J/g, and thermal conductivity ~354 W/m/K, despite starting from low-crystallinity materials (IG:ID~5). The processed CNTFs are more versatile than comparable carbon fiber, Zylon and Dyneema. Based on evidence of load transfer efficiency on individual CNTs measured with In-Situ-Stretching-Raman, we find the main contributors to property enhancements are the increasing of the effective tube contribution, in addition to the known optimization on CNTs alignment and stacking.