Motivated by the possibility that the conductivity signatures of benzo-homologated DNA bases could be used to sequence DNA, we have investigated the conductivity properties of these bases when they are non-covalently sandwiched between two (5,5) nanotube electrodes. It is found that these bases conduct poorly, making it very difficult to distinguish them. An analysis of the changes in the conductivity of benzo-adenine as a function of the distance between the tips of the nanotubes revealed that, even though the conductance increases by four orders of magnitude when the electrodes are brought closer together, the net conductance remains rather small. These results suggest that benzo-homologated bases, despite having smaller HOMO-LUMO gaps than their natural counterparts, when non-covalently bound to the electrodes cannot be used to sequence DNA by means of conductivity measurements.