The influence of backbone composition on the physical properties of donor-acceptor (D-A) copolymers composed of varying amounts of benzodithiophene (BDT) donor with the thienoisoindoledione (TID) acceptor is investigated. First, the synthesis of bis- and tris-BDT monomers is reported; these monomers are subsequently used in Stille copolymerizations to create well-defined alternating polymer structures with repeating (D-A), (D-D-A), and (D-D-D-A) units. For comparison, five semi-random D-A copolymers with a D:A ratio of 1.5, 2, 3, 4, and 7 were synthesized by reacting trimethyltin-functionalized BDT with various ratios of iodinated BDT and brominated TID. While the HOMO levels of all the resultant polymers are very similar, a systematic red shift in the absorbance spectra onset of the D-A copolymer films from 687 to 883 nm is observed with increasing acceptor content, suggesting the LUMO can be fine-tuned over a range of 0.4 eV. When the solid-state absorbance spectra of well-defined alternating copolymers are compared to those of semi-random copolymers with analogous D:A ratios, the spectra of the alternating copolymers are significantly more red-shifted. Organic photovoltaic device efficiencies show that the semi-random materials all outperform the well-defined alternating copolymers, and an optimal D:A ratio of 2 produces the highest efficiency. Additional considerations concerning fine-tuning the lifetimes of the photoconductance transients of copolymer:fullerene films measured by time-resolved microwave conductivity are discussed. Overall, the results of this work indicate that the semi-random approach is a powerful synthetic strategy for fine-tuning the optoelectronic and photophysical properties of D-A materials for a number of systematic studies, especially given the ease with which the D:A ratios in the semi-random copolymers can be tuned.