We have prepared flexible, transparent, and very conducting thin composite films from poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate), filled with both arc discharge and HIPCO single-walled nanotubes, at high loading level. The films are of high optical uniformity. The arc discharge nanotube-filled composites were significantly more conductive, demonstrating DC conductivities of >10(5) S/m for mass fractions >50 wt %. The ratio of DC to optical conductivity was higher for composites with mass fractions of 55-60 wt % than for nanotube-only films. For an 80 nm thick composite, filled with 60 wt % arc discharge nanotubes, this conductivity ratio was maximized at sigma(DC)/sigma(Op) = 15. This translates into transmittance (550 nm) and sheet resistance of 75 and 80 Omega/square, respectively. These composites were electromechanically very stable, showing <1% resistance change over 130 bend cycles.