Managing test specifications--both multiple nonstatistical constraints and flexibly defined constraints--has become an important part of designing item selection procedures for computerized adaptive tests (CATs) in achievement testing. This study compared the effectiveness of three procedures: constrained CAT, flexible modified constrained CAT, and the weighted penalty model in balancing multiple flexible constraints and maximizing measurement precision in a fixed-length CAT. The study also addressed the effect of two different test lengths--25 items and 50 items--and of including or excluding the randoms item exposure control procedure with the three methods, all of which were found effective in selecting items that met flexible test constraints when used in the item selection process for longer tests. When the randoms method was included to control for item exposure, the weighted penalty model and the flexible modified constrained CAT models performed better than did the constrained CAT procedure in maintaining measurement precision. When no item exposure control method was used in the item selection process, no practical difference was found in the measurement precision of each balancing method. (Contains 5 tables and 5 figures.)