While varying the size and branching of solubilizing side chains in g-conjugated polymers impacts their self-assembling properties in thin-film devices, these structural changes remain difficult to anticipate. This report emphasizes the determining role that linear side-chain substituents play in poly(benzo[1,2-b:4,5-b']dithiophene-thieno[3,4-c]pyrrole-4,6-dione) (PBDTTPD) polymers for bulk heterojunction (BHJ) solar cell applications. We show that replacing branched side chains by linear ones in the BDT motifs induces a critical change in polymer self-assembly and backbone orientation in thin films that correlates with a dramatic drop in solar cell efficiency. In contrast, we show that for polymers with branched alkyl-substituted BDT motifs, controlling the number of aliphatic carbons in the linear N-alkyl-substituted TPD motifs is a major contributor to improved material performance. With this approach, PBDTTPD polymers were found to reach power conversion efficiencies of 8.5% and open-circuit voltages of 0.97 V in BHJ devices with PC71BM, making PBDTTPD one of the best polymer donors for use in the high-band-gap cell of tandem solar cells.