Given a parallel corpus, semantic projection attempts to transfer semantic role annotations from one language to another, typically by exploiting word alignments. In this paper, we present an improved method for obtaining constituent alignments between parallel sentences to guide the role projection task. Our extensions are twofold: (a) we model constituent alignment as minimum weight edge covers in a bipartite graph, which allows us to find a globally optimal solution efficiently; (b) we propose tree pruning as a promising strategy for reducing alignment noise. .