We consider a discrete Schrödinger operator J whose potential is the sum of a Wigner-von Neumann term c sin(2ωn+δ)/n and a summable term. The essential spectrum of the operator J is equal to the interval [-2, 2]. Inside this interval, there are two critical points ±2 where eigenvalues may be situated. We prove that, generically, the spectral density of J has zeroes of the power {pipe}c{pipe}/2{pipe}sin ω{pipe} at these points.