Parser disambiguation with precision grammars generally takes place via statistical ranking of the parse yield of the grammar using a supervised parse selection model. In the standard process, the parse selection model is trained over a hand-disambiguated treebank, meaning that without a significant investment of effort to produce the treebank, parse selection is not possible. Furthermore, as treebanking is generally streamlined with parse selection models, creating the initial treebank without a model requires more resources than subsequent treebanks. In this work, we show that, by taking advantage of the constrained nature of these HPSG grammars, we can learn a discriminative parse selection model from raw text in a purely unsupervised fashion. This allows us to bootstrap the treebanking process and provide better parsers faster, and with less resources. 1