Suppose that Yn is obtained by observing a uniform Bernoulli random vector Xn through a binary symmetric channel with crossover probability α. The “most informative Boolean function” conjecture postulates that the maximal mutual information between Yn and any Boolean function b(Xn) is attained by a dictator function. In this paper, we consider the “complementary” case in which the Boolean function is replaced by f : {0, 1}n → {0, 1}n−1, namely, an n − 1 bit quantizer, and show that I(f(Xn); Yn) ≤ (n − 1)·(1 − h(α)) for any such f. Thus, in this case, the optimal function is of the form f (xn) = (x1,…, xn−1).