With the advent of modern computer technology, there have been growing e3orts in recent years to computerize standardized tests, including the popular Graduate Record Examination (GRE), the Graduate Management Admission Test (GMAT) and the Test of English as a Foreign Language (TOEFL). Many of such computer-based tests are known as the computerized adaptive tests, a major feature of which is that, depending on their performance in the course of testing, di3erent examinees may be given with di3erent sets of items (questions). In doing so, items can be e>ciently utilized to yield maximum accuracy for estimation of examinees’ ability traits. We consider, in this article, one type of such tests where test lengths vary with examinees to yield approximately same predetermined accuracy for all ability traits. A comprehensive large sample theory is developed for the expected test length and the sequential point and interval estimates of the latent trait. Extensive simulations are conducted with results showing that the large sample approximations are adequate for realistic sample sizes.