Indices of positive and negative agreement for observer reliability studies, in which neither observer can be regarded as the standard, have been proposed. In this article, it is demonstrated by means of an example and a small simulation study that a recently published method for constructing confidence intervals for these indices leads to intervals that are too wide. Appropriate asymptotic (i.e., large sample) variance estimates and confidence intervals for the positive and negative agreement indices are presented and compared with bootstrap confidence intervals. We also discuss an alternative method of interval estimation motivated from a Bayesian viewpoint. The asymptotic intervals performed adequately for sample sizes of 200 or more. For smaller samples, alternative confidence intervals such as bootstrap intervals or Bayesian intervals should be considered.