Given an eventually disconjugate second-order self-adjoint difference equation Δ(c_nΔ_n) + a_nn+1 = 0, where c_n ≠ 0 and is not assumed to be positive, this paper studies the eventual disconjugacy of the perturbed difference equation Δ(c_nΔy_n) + (a_n + f_n)y_n+1 = 0. Analogous to a theorem of Willett for corresponding differential equations, a necessary and sufficient condition for eventual disconjugacy in terms of a convergent sequence of averaged sums of f_n is obtained.