To guide the choice of future synthetic targets for single-molecule electronics, qualitative design rules are needed, which describe the effect of modifying chemical structure. Here the effect of heteroatom substitution on destructive quantum interference (QI) in single-molecule junctions is, for the first time experimentally addressed by investigating the conductance change when a "parent" meta-phenylene ethylene-type oligomer (m-OPE) is modified to yield a "daughter" by inserting one nitrogen atom into the m-OPE core. We find that if the substituted nitrogen is in a meta position relative to both acetylene linkers, the daughter conductance remains as low as the parent. However, if the substituted nitrogen is in an ortho position relative to one acetylene linker and a para position relative to the other, destructive QI is alleviated and the daughter conductance is high. This behavior contrasts with that of a para-connected parent, whose conductance is unaffected by heteroatom substitution. These experimental findings are rationalized by transport calculations and also agree with recent "magic ratio rules", which capture the role of connectivity in determining the electrical conductance of such parents and daughters.