question on set theory

This question is not category theory, but I am sure there are people on the net who know much more set theory than me. If you assume the generalized continuum hypothesis, it is evident that any power cardinal $\kappa$ has the property that $\lambda < \kappa$ implies $2^\lambda <= \kappa$. Otherwise, that property is obvious to me only for inaccessible cardinals. My question is whether there are a large class of cardinals for which that is true even without the GCH? Michael