A single saddlepoint approximation for call prices seen as complementary probabilities that log price exceeds log strike by an independent exponential under the share measure is developed using a non-Gaussian base. The suggested base is that of a Gaussian random variable less an exponential with parameter λ. It is suggested that λ be chosen to match the volatility under the share measure. The method is implemented and observed to be exact for the Black-Scholes model. Six other models with closed forms for the cumulant generating function are also investigated.