We apply the well-known parsing technique of self-training to a new type of text: language-learner text. This type of text often contains grammatical and other errors which can cause problems for traditional treebank-based parsers. Evaluation on a small test set of student data shows improvement over the baseline, both by training on native or non-native text. The main contribution of this paper adds additional support for the claim that the new self-trained parser has improved over the baseline by carrying out a qualitative linguistic analysis of the kinds of differences between two parsers on non-native text. We show that for a number of linguistically interesting cases, the self-trained parser is able to provide better analyses, despite the sometimes ungrammatical nature of the text. 1