A major goal of axion searches is to reach inside the parameter space region of realistic axion models. Currently, the boundaries of this region depend on somewhat arbitrary criteria, and it would be desirable to specify them in terms of precise phenomenological requirements. We consider hadronic axion models and classify the representations RQ of the new heavy quarks Q. By requiring that i) the Q are sufficiently short lived to avoid issues with long lived strongly interacting relics, ii) no Landau poles are induced below the Planck scale, fifteen cases are selected, which define a phenomenologically preferred axion window bounded by a maximum (minimum) value of the axion-photon coupling about twice (four times) larger than commonly assumed. Allowing for more than one RQ, larger couplings, as well as complete axion-photon decoupling, become possible.