A possible role of impurities in the well‐known difficulty of obtaining well‐conducting large‐band‐gap material is investigated. Specifically, the limitations imposed on carrier concentrations by chemical equilibrium considerations are analyzed for a (model) system of a single amphoteric impurity. It is also shown that energies of formation of at least some Group‐I interstitials in a typical II–VI semiconductor, ZnSe, are expected to be low compared to those of native donor defects. Since Group‐I impurities act as acceptors on a metal substitutional site, but as donors when on a interstitial site, a stable interstitial form results in amphoteric behavior and thus in constraints on achievable carrier concentrations if such impurities are present either deliberately or accidentally.