Summary: The problem of ranking the K-best binary trees with respect to their weighted average leaves' levels is considered. Both the alphabetic case, where the order of the weights in the sequence \(w_ 1,...,w_ n\) must be preserved in the leaves of the tree, and the nonalphabetic case, where no such restriction is imposed, are studied. For the alphabetic case a simple algorithm is provided for ranking the K-best trees based on a recursive formula of complexity \(0(Kn^ 3)\). For nonalphabetic trees two different ranking problems are considered, and for each of them it is shown that the next best tree can be solved by a dynamic programming formula of low complexity order.