Dispersing carbon nanotubes (CNTs) using surfactants into water requires ultrasonication that supplies mechanical energy to debundle and exfoliate CNTs. However, sonication is known to damage CNTs and to cut them into short fragments. Also, the CNT concentration in water dispersion is typically limited to up to 1.0 wt %. Here, we show that by using a sulfuric acid pretreatment, we can enhance the debundling of CNTs and reduce subsequent sonication to achieve homogeneous dispersions without damaging CNTs. Additionally, using a progressive and controlled dialysis, we are able to increase the CNT concentration up to 1.8 wt %. We demonstrate that such highly concentrated dispersions can be used as spin dopes to fabricate continuous fibers. Our fibers have an electrical conductivity up to 580 kS/m, a tensile strength of similar to 1 GPa, and a Young's modulus of 123 GPa, exceeding the mechanical properties of related fibers made from conventional surfactant-stabilized dispersions of sonicated CNTs.