We consider the role of dispersive contributions in the analysis of the KL-KS system. These long-distance pieces can be present in both the real and imaginary parts of the mixing element M12. We provide an estimate of one such effect in Im M12, the η′ pole, which turns out to be potentially significant. These terms can substantially modify phenomenological studies, as we demonstrate for several cases. Improved experimental bounds on ε′/ε can provide a strong limit on dispersive effects in Im M12, and may in the near future remove the uncertainties caused by these contributions.