A parsing system returning analyses in the form of sets of grammatical relations can obtain high precision if it hypothesises a particular relation only when it is certain that the relation is correct. We operationalise this technique--in a statistical parser using a manually-developed wide-coverage grammar of English--by only returning relations that form part of all analyses licensed by the grammar. We observe an increase in precision from 75% to over 90% (at the cost of a reduction in recall) on a test corpus of naturally-occurring text.