A boolean predicate f:01k01 is said to be {\em somewhat approximation resistant} if for some constant \frac{|f^{-1}(1)|}{2^k}">2kf−1(1), given a -satisfiable instance of the MAX-k-CSP(f) problem, it is NP-hard to find an assignment that {\it strictly beats} the naive algorithm that outputs a uniformly random assignment. Let (f) denote the supremum over all for which this holds. It is known that a predicate is somewhat approximation resistant precisely when its Fourier degree is at least 3. For such predicates, we give a characterization of the {\it hardness gap} ((f)−2kf−1(1)) up to a factor of O(k5). We also give a similar characterization of the {\it integrality gap} for the natural SDP relaxation of MAX-k-CSP(f) after (n) rounds of the Lasserre hierarchy.