Various models of Markov-renewal programming were presented in a previous work. Related models have been presented independently by de Cani, Howard, and Schweitzer. Since that time, new results have been obtained which clarify certain questions raised in these papers. Since these results are either 'in the folklore,' or are available only in scattered unpublished reports, it seemed worthwhile to gather them together in one article. This article considers only the finite-state, finite alternative space, infinite- horizon, undiscounted and discounted models previously discussed.