Assume we want to test a null hypothesis about a single mean at = .05, one-tailed.

Assume we want to test a null hypothesis about a single mean at α = .05, one-tailed. Further assume that all necessary assumptions are met. Is there ever a case in which we are more likely to reject a true H₀ than we are to reject H₀ if it is false? (In other words, can power ever be less than a?)