As previously argued, the correlation between included and omitted regressors generally causes inconsistency of standard estimators for count data models. Using a specific residual function and suitable instruments, a consistent generalized method of moments estimator can be obtained under conditional moment restrictions. This approach is extended here by fully exploiting the model assumptions and thereby improving efficiency of the resulting estimator. Empirical likelihood estimation in particular has favorable properties in this setting compared to the two-step GMM procedure, which is demonstrated in a Monte Carlo experiment. The proposed method is applied to the estimation of a cigarette demand function.