One of the basic tasks for Bayesian networks (BNs) is that of learning a\nnetwork structure from data. The BN-learning problem is NP-hard, so the\nstandard solution is heuristic search. Many approaches have been proposed for\nthis task, but only a very small number outperform the baseline of greedy\nhill-climbing with tabu lists; moreover, many of the proposed algorithms are\nquite complex and hard to implement. In this paper, we propose a very simple\nand easy-to-implement method for addressing this task. Our approach is based on\nthe well-known fact that the best network (of bounded in-degree) consistent\nwith a given node ordering can be found very efficiently. We therefore propose\na search not over the space of structures, but over the space of orderings,\nselecting for each ordering the best network consistent with it. This search\nspace is much smaller, makes more global search steps, has a lower branching\nfactor, and avoids costly acyclicity checks. We present results for this\nalgorithm on both synthetic and real data sets, evaluating both the score of\nthe network found and in the running time. We show that ordering-based search\noutperforms the standard baseline, and is competitive with recent algorithms\nthat are much harder to implement.\n