Let p be a prime and q = p ^s and ζ_k a fixed primitive kth root of unity in some extension of Q. Let χ be a multiplicative character over F_q of order k and J (χ, χ) the associated Jacobi sum. We give examples of χ which satisfy J (χ, χ) ∈p ^[s/2]Z[ζ_k]. Moreover, for s = 3, we prove that there is only a finite number of k such that J(χ, χ) is an element of pZ[ζ_k] except for the case where k is divisible by nine and p ≡1 ± k/3 (mod k).