In this study we synthesized medium-band gap, two-dimensional (2-D) conjugated polymers comprising electron-rich benzo[1,2-b:4,5-b′]dithiophene (BDT) units presenting conjugated thiophene (T) side chains and electron-deficient alkoxy-modified 2,1,3-benzooxadiazole (BO) moieties. We introduced various solubilizing substituents - linear alkyl, alkoxy, and alkythio units - on the thiophene side chains to obtain a series of 2-D conjugated D-π-A polymers: PBDTT-C-BO, PBDTT-O-BO, and PBDTT-S-BO. The solubilizing substituents of the BDT units altered the solubility, conformations, and electronic properties of the synthesized conjugated polymers, allowing tuning of the photovoltaic properties when blended with fullerenes. We investigated the effects of the different linear solubilizing substituents of the BDT units on the structural, optical, and electronic properties (e.g., band gap energies) of the resulting 2-D conjugated polymers, as determined from quantum-chemical calculations, UV-Vis absorption spectra, and grazing-incidence X-ray diffraction. Atomic force microscopy and transmission electron microscopy images revealed the morphologies of active layers comprising these 2-D conjugated polymers and the fullerene derivative [6,6]-phenyl-C71-butyric acid methyl ester (PC71BM). Through rational structural modifications of the solubilizing substituents in the 2-D conjugated polymers with alkoxy, alkythio or alkyl units, the resulting PCEs varied from 5.4 to 7.5%. A polymer solar cell based on a blend of PBDTT-C-BO and PC71BM exhibited the best photovoltaic performance among our three studied systems, with a high short-circuit current density (Jsc) of 15.7 mA cm-2 and a power conversion efficiency of 7.5%, without the need for any processing additives or post-treatment processes, highlighting the importance of careful selection of appropriate solubilizing substituent that attached to the donor segments when designing efficient D-π-A polymers for use in solar cells.