Phylogenetic analysis is used in all branches of biology with applications ranging from studies on the origin of human populations to investigations of the transmission patterns of HIV. Most phylogenetic analyses rely on effective heuristics for obtaining accurate trees. However, relatively little work has been done to analyze quantitatively the behavior of phylogenetic heuristics in tree space. A better understanding of local search behavior can facilitate the design of better heuristics, which ultimately lead to more accurate depictions of the true evolutionary relationships. In this paper, we present new and novel insights into local search behavior for maximum parsimony on three biological datasets consisting of 44, 60, and 174 taxa. By analyzing all trees from search, we find that, as the search algorithm climbs the hill to local optima, the trees in the neighborhood surrounding the current solution improve as well. Furthermore, the search is quite robust to a small number of randomly selected neighbors. Thus, our work shows how to gain insights into the behavior of local search algorithm by exploring a large diverse collection of trees.