We consider some nonnormal regression situations in which there are many regressor variables, and it is desired to determine good fitting models, according to the value of the likelihood ratio statistic for tests of submodels against the full model. Efficient computational algorithms for the normal linear model are adopted for use with nonnormal models. Even with as many as 10-15 regressor variables present, we find it is often possible to determine all of the better fitting models with relatively small amounts of computer time. The use of the procedures is illustrated on exponential, Poisson and binary regression models.