We report the production and characterization of polymer nanocomposites with single-walled carbon nanotubes having improved mechanical properties and exceptional nanotube alignment. High-pressure carbon monoxide nanotubes (HiPco) were efficiently distributed in polystyrene (PS) and polyethylene (PE) with a twin-screw compounder. Nanotube concentrations were 1, 5, 10, and 20 wt% in PE composites and 0.7 wt% in PS composites. PE composites were melt-spun into fibers to achieve highly aligned nanotubes. Polarized Raman spectroscopy shows that the degree of alignment increases with decreasing fiber diameter and decreases with increasing nanotube loading. The orientation distribution function of a 1 wt% HiPco/PE composite had a full width at half-maximum of approximately 5 degrees. The elastic modulus increases up to 450% relative to PE fibers for 20 wt% nanotube loading at an intermediate fiber diameter of 100 microns.