Logistic regression has become increasingly popular for modeling nest success in terms of nest-specific explanatory variables. However, logistic regression models for nest fate are inappropriate when applied to data from nests found at various ages, for the same reason that the apparent estimator of nest success is biased (i.e. older clutches are more likely to be successful than younger clutches). A generalized linear model is presented and illustrated that gives ornithologists access to a flexible, suitable alternative to logistic regression that is appropriate when exposure periods vary, as they usually do. Unlike the Mayfield method (1961, 1975) and the logistic regression method of Aebischer (1999), the logistic-exposure model requires no assumptions about when nest losses occur. Nest survival models involving continuous and categorical explanatory variables, multiway classifications, and time-specific (e.g. nest age) and random effects are easily implemented with the logistic-exposure model. Application of the model to a sample of Yellow-breasted Chat (Icteria virens) nests shows that logistic-exposure estimates for individual levels of categorical explanatory variables agree closely with estimates obtained with Johnson (1979) constant-survival estimator. Use of the logistic-exposure method to model time-specific effects of nest age and date on survival of Blue-winged Teal (Anas discors) and Mallard (A. platyrhynchos) nests gives results comparable to those reported by Klett and Johnson (1982). However, the logistic-exposure approach is less subjective and much easier to implement than Klett and Johnson's method. In addition, logistic-exposure survival rate estimates are constrained to the (0,1) interval, whereas Klett and Johnson estimates are not. When applied to a sample of Mountain Plover (Charadrius montanus) nests, the logistic-exposure method gives results either identical to, or similar to, those obtained with the nest survival model in program MARK (White and Burnham 1999). I illustrate how the combination of generalized linear models and information-theoretic techniques for model selection, along with commonly available statistical software, provides ornithologists with a powerful, easily used approach to analyzing nest success.