In 1983, Horowitz proposed the use of an adjusted likelihood ratio index to select between alternative models. We define an alternative index based on the Akaike Information Criterion. The two indices incorporate different degrees-of-freedom corrections to the same measure of goodness-of-fit. The Akaike index favors more parsimonious models. We argue that the Akaike measure is the appropriate criterion for model selection. We utilize Horowitz's results on non-nested hypothesis testing for the new index.