We say that a subshift, i.e. a closed shift invariant subspace of the space of sequences on a finite alphabet, has bounded powers. If there is an upper bound on the powers n with which words occur in the subshift. This is a strong combinatorial property which, for Sturmian susbshifts, coincides with the fact that the slope has bounded continued fraction expansion. Approximating the subshift space by a family of graphs we obtain a family of metrics which may or may not be Lipschitz equivalent. That latter property turns out to charactise minimal subshifts which have bounded powers.