It is not uncommon to use unidimensional item response theory models to estimate ability in multidimensional data with computerized adaptive testing (CAT). The current Monte Carlo study investigated the penalty of this model misspecification in CAT implementations using different item selection methods and exposure control strategies. Three item selection methods—maximum information (MAXI), a-stratification (STRA), and a-stratification with b-blocking (STRB) with and without Sympson–Hetter (SH) exposure control strategy—were investigated. Calibrating multidimensional items as unidimensional items resulted in inaccurate item parameter estimates. Therefore, MAXI performed better than STRA and STRB in estimating the ability parameters. However, all three methods had relatively large standard errors. SH exposure control had no impact on the number of overexposed items. Existing unidimensional CAT implementations might consider using MAXI only if recalibration as multidimensional model is too expensive. Otherwise, building a CAT pool by calibrating multidimensional data as unidimensional is not recommended.