Multistage blood pressure screening rules are often used to select subjects for clinical trials. Multiple blood pressure readings are taken over successive visits, and the subject must meet eligibility criteria at each visit. In this paper, the authors present methods which depend on the distribution of the subject's underlying blood pressure values (the predictive value approach) or, alternatively, the subject's observed mean over all screening visits (the empirical predictive value approach) given the observed mean after one or more visits. The authors apply these methods to data from Phase I of the Trials of Hypertension Prevention, which attempts to identify subjects with mean diastolic blood pressures in the range 80-89 mmHg over three screening visits. The estimated efficiency of these rules is evaluated in terms of the number of clinic screening visits needed per eligible subject. Relative to reexamining all subjects at each visit (no screening), these approaches can reduce the number of visits required by 27%. This is in contrast to the standard rule in which a subject must have an observed mean diastolic blood pressure of 80-89 mmHg on each of three consecutive visits, which requires twice as many clinic visits per eligible subject as not screening. Thus, the approach presented is useful in identifying eligible subjects for clinical trials in an efficient manner.