Abstract. Let / be an ideal in a Noetherian domain R, and let / be the integral closure of /. Let A*(I) = A^s(R/I") for n large (it being known that for large n this set does not vary with n). Suppose that R satisfies the altitude formula. Then it is shown that P e Â*(I) if and only if height P ■> l(IP), the analytic spread of /,,.