New donor–acceptor-type copolymers comprised of benzobisthiazole (BBTz) as a weak donor rather than acceptor are proposed. This approach can simultaneously lead to deepening the HOMO and LUMO of the polymers with moderate energy offset against fullerene derivatives in bulk heterojunction organic photovoltaics. As a proof-of-concept, BBTz-based random copolymers conjugated with typical electron acceptors: thienopyrroledione (TPD) and benzothiadiazole (BT) based on density functional theory calculations are synthesized. Laser-flash and Xe-flash time-resolved microwave conductivity (TRMC) evaluations of polymer:[6,6]-phenyl C61 butyric acid methyl ester (PCBM) blends are conducted to screen the feasibility of the copolymers, leading to optimization of processing conditions for photovoltaic device application. According to the TMRC results, alternating BBTz-BT copolymers are designed, exhibiting extended photoabsorption up to ca. 750 nm, deep HOMO (–5.5 to –5.7 eV), good miscibility with PCBM, and inherent crystalline nature. Moreover, the maximized PCE of 3.8%, the top-class among BBTz-based polymers reported so far, is realized in an inverted cell using TiOx and MoOx as the buffer layers. This study opens up opportunities to create low-bandgap polymers with deep HOMO, and shows how the device-less TRMC evaluation is of help for decision-making on judicious molecular design.