We show how partial models of natural language syntax (manually written DCGs, with parameters estimated from a parsed corpus) can be automatically extended when trained upon raw text (using MDL). We also show how we can use a parsed corpus as an alternative constraint upon learning. Empirical evaluation suggests that a parsed corpus is more informative than a MDL-based prior. However, best results are achieved when the learner is supervised with a compressionbased prior and a parsed corpus.