A population survey for estimating prevalence is challenging when a disease or condition is difficult to diagnose. If clinical diagnosis is expensive, a 2-phase study, in which less expensive but less accurate tests are administered to all study subjects in the first phase (screening phase) and a more accurate but expensive or time-consuming test is administered to only a subset of the subjects in the second phase, is an attractive approach. Published research has discussed ways of maximizing precision of the prevalence estimate from a 2-phase study with a "gold standard" second-phase test. For many psychiatric disorders, even the best diagnostic tests are not of gold standard quality. In this paper, the authors propose a quasi-optimal design for 2-phase prevalence studies without a gold standard test; random-effects latent class analysis facilitates the estimation of prevalence and appropriately addresses the issue of dependent errors among the diagnostic tests. The authors show that the quasi-optimal design is efficient compared with the balanced and random designs when there is strong inter-test dependence caused by additional factors, apart from disease status, and highlight the importance of collecting data on those subjects testing negative in the first phase.