While polymer acceptors are promising fullerene alternatives in the fabrication of efficient bulk heterojunction (BHJ) solar cells, the range of efficient material systems relevant to the “all-polymer” BHJ concept remains narrow, and currently limits the perspectives to meet the 10% efficiency threshold in all-polymer solar cells. This report examines two polymer acceptor analogs composed of thieno[3,4-c]pyrrole-4,6-dione (TPD) and 3,4-difluorothiophene ([2F]T) motifs, and their BHJ solar cell performance pattern with a low-bandgap polymer donor commonly used with fullerenes (PBDT-TS1; taken as a model system). In this material set, the introduction of a third electron-deficient motif, namely 2,1,3-benzothiadiazole (BT), is shown to (i) significantly narrow the optical gap (Eopt) of the corresponding polymer (by ≈0.2 eV) and (ii) improve the electron mobility of the polymer by over two orders of magnitude in BHJ solar cells. In turn, the narrow-gap P2TPDBT[2F]T analog (Eopt = 1.7 eV) used as fullerene alternative yields high open-circuit voltages (VOC) of ≈1.0 V, notable short-circuit current values (JSC) of ≈11.0 mA cm−2, and power conversion efficiencies (PCEs) nearing 5% in all-polymer BHJ solar cells. P2TPDBT[2F]T paves the way to a new, promising class of polymer acceptor candidates.