Two regioregular narrow band gap conjugated polymers with a D’-A-D-A repeat unit architecture, namely PIFCF and PSFCF, were designed and synthesized. Both polymers contain strictly organized fluorobenzo[c][1,2,5]thiadiazole (FBT) orientations and different solubilizing side chains for solution processing. Compared to the previously reported asymmetric pyridyl-[2,1,3]thiadiazole (PT) based regioregular polymer, namely PIPCP, PIFCF and PSFCF exhibit wider band gaps, tighter π-π stacking, and improved hole mobilities. When incorporated into solar cells with fullerene acceptors, the Eloss = Eg - eVoc values of PIFCF and PSFCF devices are increased compared to solar cells based on PIPCP. Determination of Ect in these solar cells reveals that, relative to PIPCP, PIFCF solar cells lose more energy from Eg - Ect, and PSFCF solar cells lose more energy from both Eg - Ect and Ect - eVoc. The close structural relationship between PIPCP and PIFCF provides an excellent framework to establish molecular features that impact the relationship between Eg and Ect. Theoretical calculations predict that Eloss of PIFCF:PC61BM would be higher than in the case of PIPCP:PC61BM, due to greater Eg - Ect. These findings provide insight into the design of high performance, low voltage loss photovoltaic polymeric materials with desirable optoelectronic properties.