We discuss the power counting for effective field theories with narrow
resonances near a two-body threshold. Close to threshold, the effective field
theory is perturbative and only one combination of coupling constants is
fine-tuned. In the vicinity of the resonance, a second, ``kinematic''
fine-tuning requires a nonperturbative resummation. We illustrate our results
in the case of nucleon-alpha scattering.Comment: 11 pages, revtex4, 3 ps figure