We describe a conjugated statistical copolymer, poly(3-hexylthiophene)-stat-(3-thiohexylthiophene) (P3HT-s-P3THT), with 3-hexylthiophene:3-thiohexylthiophene monomer ratios ranging from 50:50 to 99:1. The copolymer is head-to-tail regioregular in both its hexylthiophene-hexylthiophene and hexylthiophene-thiohexylthiophene linkages, which is not observed in poly(3-thioalkylthiophene) homopolymers. The polymer sequence is random, and the H-1 NMR spectra have eight distinct aromatic signals that correspond to the eight possible HT-HT regioisomer triads and differ from the spectra expected for the corresponding block or homopolymer systems. When testing the copolymers in bulk heterojunction devices with a fullerene-derivative (PC71BM) acceptor, the copolymers have an 11-18% increase in the open-circuit voltage (V-oc) relative to the P3HT:PC71BM device due to the deeper HOMO level of the 3-thiohexylthiophene unit. This increase is independent of copolymer composition over the 50:50 to 85:15 range and is still observed when there is just one 3-thiohexylthiophene unit in the polymer chain. This shows that statistical copolymers containing as low as 1% of a deep HOMO unit can be used to increase the V-oc of the device relative to the parent polymer. All device parameters change in a nonlinear manner as a function of composition, which highlights the distinct properties that can be achieved with conjugated statistical copolymers.