Markov trees generalize naturally to bounded tree-width Markov networks, onwhich exact computations can still be done efficiently. However, learning themaximum likelihood Markov network with tree-width greater than 1 is NP-hard, sowe discuss a few algorithms for approximating the optimal Markov network. Wepresent a set of methods for training a density estimator. Each method isspecified by three arguments: tree-width, model scoring metric (maximumlikelihood or minimum description length), and model representation (using onejoint distribution or several class-conditional distributions). On thesemethods, we give empirical results on density estimation and classificationtasks and explore the implications of these arguments.