Two C-60 dumbbell molecules have been synthesized containing either cyclopropane or pyrrolidine rings connecting two fullerenes to a central fluorene core. A combination of spectroscopic techniques reveals that the cyclopropane dumbbell possesses better electronic communication between the fullerenes and the fluorene. This observation is underpinned by DFT transport calculations, which show that the cyclopropane dumbbell gives a higher calculated single-molecule conductance, a result of an energetically lower-lying LUMO level that extends deeper into the backbone. This strengthens the idea that cyclopropane behaves as a quasi-double bond.