The exact saddlepoint approximation as developed by Daniels [4], is an extremely accurate method for approximating probability distributions. Recent applications of the technique to densities of statistics of interest have been hindered by the requirement of explicit knowledge of the cumulant generating function, and the need to obtain an analytic solution to the saddlepoint defining equation. In this paper we show the conditions under which any approximation to the saddlepoint is justified, and suggest a solution that does not affect the usual merits of the exact expansion. We illustrate with an approximate saddlepoint expansion of the Durbin-Watson test statistic.