Model-based approaches to automatic target recognition (ATR) generally infer the class and pose of objects in imagery by exploiting theoretical models of the formed images. Recently, we have performed an evaluation of several statistical models for synthetic aperture radar (SAR) and have conducted experiments with ATR algorithms derived from these models. In particular, a one-parameter complex Gaussian model, classically used to model diffuse scattering, was shown to deliver higher recognition rates than a one-parameter quarter-power normal model on actual SAR data. However an extended, two-parameter quarter-power model was consistently a better fit to the data than a corresponding two-parameter Gaussian model. In this paper, we apply Rician, gamma, and K distribution models, which are two-parameter extensions of the complex Gaussian and quarter-power normal models, to ATR from SAR magnitude imagery. We consider maximum-likelihood estimation of unknown model parameters and apply the resulting training and testing algorithms to actual SAR data. We show that the K distribution model performs better than the Rician and gamma models for both large and small sample sizes. The one-parameter complex Gaussian model performed slightly better than the K model overall. For small sample sizes, this is likely due to the relative stability in estimating only one model parameter. For large sample sizes this is likely due to a lack of persistence in specular reflections over the large angular intervals required to obtain large samples.