Abstract Marginal MAP is known to be a difficult task for graphical models, particularly because the evaluation of each MAP assignment involves a conditional likelihood computation. In order to minimize the number of likelihood evaluations, we focus in this paper on best-first search strategies for exploring the space of partial MAP assignments. We analyze the potential relative benefits of several bestfirst search algorithms and demonstrate their effectiveness against recent branch and bound schemes through extensive empirical evaluations. Our results show that best-first search improves significantly over existing depth-first approaches, in many cases by several orders of magnitude, especially when guided by relatively weak heuristics.