Interest in developing computerized adaptive testing (CAT) under cognitive diagnosis models (CDMs) has increased recently. CAT algorithms that use a fixed-length termination rule frequently lead to different degrees of measurement precision for different examinees. Fixed precision, in which the examinees receive the same degree of measurement precision, is a major advantage of CAT over nonadaptive testing. In addition to the precision issue, test security is another important issue in practical CAT programs. In this study, the authors implemented two termination criteria for the fixed-precision rule and evaluated their performance under two popular CDMs using simulations. The results showed that using the two criteria with the posterior-weighted Kullback-Leibler information procedure for selecting items could achieve the prespecified measurement precision. A control procedure was developed to control item exposure and test overlap simultaneously among examinees. The simulation results indicated that in contrast to no method of controlling exposure, the control procedure developed in this study could maintain item exposure and test overlap at the prespecified level at the expense of only a few more items.