The computer program of McClellan, Parks and Rabiner [1] for designing optimal (minimax) FIR filters requires the order of the filter as an input parameter. Although a reliable estimate for the lowpass case is known [2], no such estimate exists for the bandpass case. In this paper we investigate the problem of estimating the order of an optimal bandpass filter. The effects of the design specifications on filter order are studied, and a simple estimate of the filter order is presented.