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The inside-outside algorithm for inferring the parameters of a stochastic context-free grammar is extended to take advantage of constituent information (constituent bracketing) in a partially parsed corpus. Experiments on formal and natural language parsed corpora show that the new algorithm can achieve faster convergence and better modeling of hierarchical structure than the original one. In particular, over 90% test set bracketing accuracy was achieved for grammars inferred by our algorithm from a training set of handparsed part-of-speech strings for sentences in the Air Travel Information System spoken language corpus. Finally, the new algorithm has better time complexity than the original one when sufficient bracketing is provided.