We present a stochastic parsing system consisting of a Lexical-Functional Grammar (LFG), a constraint-based parser and a stochastic disambiguation model. We report on the results of applying this system to parsing the UPenn Wall Street Journal (WSJ) treebank. The model combines full and partial parsing techniques to reach full grammar coverage on unseen data. The treebank annotations are used to provide partially labeled data for discriminative statistical estimation using exponential models. Disambiguation performance is evaluated by measuring matches of predicate-argument relations on two distinct test sets. On a gold standard of manually annotated f-structures for a subset of the WSJ treebank, this evaluation reaches 79% F-score. An evaluation on a gold standard of dependency relations for Brown corpus data achieves 76% F-score.