This project focuses on model-selection algorithms for learning Bayesian networks. The impact that the search space connectivity has on the result is investigated in some detail and general guidelines for defining efficient neighborhoods that allows optimality are developed. These guidelines are formulated in terms of local transformations on DAG Markov models, and are therefor directly applicable to many model-selection algorithms that define their neighborhood by local transformations. The quality of these guidelines has been demonstrated in the development of a stochastic equivalence search (SES) algorithm and the k-greedy equivalence search (KES) algorithm.