A fundamental problem in biological classi cation is the reconstruction of phylogenetic trees for a set X of species from a collection of either subtrees or qualitative characters. This task is equivalent to tree reconstruction from a set of partial X{splits (bipartitions of subsets of X). In this paper, we de ne and analyse a \closure" operation for partial X{splits that was informally proposed by Meacham [5]. In particular, we establish a su cient condition for such an operation to reconstruct a tree when there is essentially only one tree that displays the partial X{splits. This result exploits a recent combinatorial result from [2].