We have measured the single-molecule conductance of a family of bithiophene derivatives terminated with methyl-sulfide gold-binding linkers using a scanning tunneling microscope based break-junction technique. We find a broad distribution in the single-molecule conductance of bithiophene compared with that of a methyl-sulfide terminated biphenyl. Using a combination of experiments and calculations, we show that this increased breadth in the conductance distribution is explained by the dif-ference in 5-fold symmetry of thiophene rings as compared to the 6-fold symmetry of benzene rings. The reduced symmetry of thiophene rings results in a restriction on the torsion angle space available to these molecules when bound between two metal electrodes in a junction, causing each molecular junction to sample a different set of conformers in the conductance measurements. In contrast, the rotations of biphenyl are essentially unimpeded by junction binding, allowing each molecular junction to sample the similar conformers. This work demon-strates that the conductance of bithiophene displays a strong dependence on the conformational fluctua-tions accessible within a given junction configuration, and that the symmetry of such small molecules can significantly influence their conductance behaviors.