Suppose we are givennindependent observations (X1,Y1), …, (Xn, Yn) from a conditionally specified distribution with densityf(x, y). The problem of estimating the unknown parameters off(x, y) is complicated by the presence of an intractable normalizing constant that, in this conditional approach, is chosen so that the density integrates to 1. An approach to estimation is used here that is known to result in asymptotically efficient estimators of the unknown parameters whenf(x, y) is from an exponential family. It is an application of a method that has appeared in the literature and is due to J. K. Lindsey. It very conveniently avoids the dependence on the normalizing constants in the joint distribution. The usual maximum-likelihood estimates of the parameters can be obtained using software readily available for Poisson regression. The usefulness of this estimation method is illustrated for a model resulting from specifying that the conditionals are two-parameter, shape and scale, gamma. It is assumed that only the scale parameter depends on the conditioning variable. This model subsumes the BEC class and several characteristics of the model extend those of the BEC class.