Traditional information retrieval evaluation relies on both precision and recall. However, modern search environments such as the Web, in which recall is either unimportant or immeasurable, require precision-oriented evaluation. In particular, finding one highly relevant document is very important for practical tasks such as known-item search and suspected-item search. This paper compares the properties of five evaluation metrics that are applicable to the task of finding one highly relevant document in terms of the underlying assumptions, how the system rankings produced resemble each other, and discriminative power. We employ two existing methods for comparing the discriminative power of these metrics: The Swap Method proposed by Voorhees and Buckley at ACM SIGIR 2002, and the Bootstrap Sensitivity Method proposed by Sakai at SIGIR 2006. We use four data sets from NTCIR to show that, while P(⁺)-measure, O-measure and NWRR (Normalised Weighted Reciprocal Rank)are reasonably highly correlated to one another, P(⁺)-measure and O-measure are more discriminative than NWRR, which in turn is more discriminative than Reciprocal Rank. We therefore conclude that P(⁺)-measure and O-measure, each modelling a different user behaviour, are the most useful evaluation metrics for the task of finding one highly relevant document.