A variation of the Bourgeois-Pichat biometric analysis of infant mortality is suggested. In the original model, cumulative mortality in the last eleven months of infancy is assumed to follow a uniform distribution given a log-cube transformation of age. Instead, we assume an exponential distribution. The difference is that while the denominator is constant in the Bourgeois-Pichat model, equal to the number of births, in our model, the denominator is the current population at risk. We argue that our assumption is more satisfactory from a theoretical point of view, since it focus on the conditional probability of dying. Our model gives different estimates of endogenous and exogenous mortality and, in addition, the model fit is slightly better, especially in cases with higher levels of infant mortality.