We show that a previously proposed algorithm for the N-best trees problem can be made more efficient by changing how it arranges and explores the search space. Given an integer N and a weighted tree automaton (wta) M over the tropical semiring, the algorithm computes N trees of minimal weight with respect to M. Compared with the original algorithm, the modifications increase the laziness of the evaluation strategy, which makes the new algorithm asymptotically more efficient than its predecessor. The algorithm is implemented in the software BETTY, and compared to the state-of-the-art algorithm for extracting the N best runs, implemented in the software toolkit TIBURON. The data sets used in the experiments are wtas resulting from real-world natural language processing tasks, as well as artificially created wtas with varying degrees of nondeterminism. We find that BETTY outperforms TIBURON on all tested data sets with respect to running time, while TIBURON seems to be the more memory-efficient choice.