This paper describes the salient features of using a simulated annealing (SA) algorithm in the context of designing digital filters with coefficient values expressed as the sum of power of two. A procedure for linear phase digital filter design, using this algorithm, is first presented and tested, yielding results as good as known optimal methods. The algorithm is then applied to the design of Nyquist filters, optimizing at the same time both frequency response and intersymbol interference, and to the design of cascade form FIR filters. Although SA is not a solution to all design problems, and is computationally very expensive, it may be an important method for designing special digital filters where numerous or conflicting constraints are present.