Pseudo-Boolean methods are particularly suited to problems in which the variables take only two values, 0 and 1. In this paper, a method is presented for solving nonlinear pseudo-Boolean inequalities, and is applied to limited word length design of IIR digital filters. Starting with an approximate solution, the proposed design method adjusts the quantized coefficients to achieve the best filter characteristics. It takes much less computation time as compared to the existing search techniques and overcomes the problem of global optimum, inherent in these techniques. The use of the method is demonstrated through an example of a third order Chebyshev filter.