This paper is concerned with the problem of static output-feedback stabilization of discrete-time Lur'e systems. The control law feedbacks both the output and the nonlinearity. By using a quadratic Lyapunov function, new design conditions are provided in terms of new sufficient design linear matrix inequalities where the control gains appear affinely. Using some relaxations, the search for the stabilizing control gains is performed through an iterative algorithm. The approach can be considered as more general than the existing ones thanks to the fact that the gains are treated as decision variables in the optimization problem. Therefore, the approach can handle state or output feedback indistinctly, and can include magnitude or structural constraints (such as decentralization) on the gains. Numerical examples illustrate that the proposed method can provide less conservative results when compared with other techniques from the literature.