This paper investigates bootstrapping for statistical parsers to reduce their reliance on manually annotated training data. We consider both a mostly-unsupervised approach, co-training, in which two parsers are iteratively re-trained on each other’s output; and a semi-supervised approach, corrected co-training, in which a human corrects each parser’s output before adding it to the training data. The selection of labeled training examples is an integral part of both frameworks. We propose several selection methods based on the criteria of minimizing errors in the data and maximizing training utility. We show that incorporating the utility criterion into the selection method results in better parsers for both frameworks.