Heteroatom substitution into the cores of alternant, aromatic hydrocarbons containing only even-membered rings is attracting increasing interest as a method of tuning their electrical conductance. Here we examine the effect of heteroatom substitution into molecular cores of non-alternant hydrocarbons, containing odd-membered rings. Benzodichalcogenophene (BDC) compounds are rigid, planar π-conjugated structures, with molecular cores containing 5-membered rings fused to a 6-membered aryl ring. To probe the sensitivity or resilience of constructive quantum interference (CQI) in these non-bipartite molecular cores, two C 2 -symmetric molecules (I and II) and one asymmetric molecule (III) are investigated. I (II) contains S (O) heteroatoms in each of the 5-membered rings, while III contains an S in one 5-membered ring and an O in the other. Differences in their conductances arise primarily from the longer S-C and shorter O-C bond lengths compared with the C-C bond and the associated changes in their resonance integrals. We find that although the conductance of III is significantly lower than the conductances of the others, CQI is resilient and persists in all molecules.