We highlight the challenge of proving correlation bounds between boolean functions and integer-valued polynomials, where any non-boolean output counts against correlation. We prove that integer-valued polynomials of degree 1 2 lg2 lg2 n have zero correlation with parity. Such a result is false for modular and threshold polynomials. Its proof is based on a strengthening of an anti-concentration result by Costello, Tao, and Vu (Duke Math. J. 2006).