Traditional multiple-group CFA is usually criticized for having too restrictive model assumption, namely the scalar measurement invariance. The new multiple-group analysis method, alignment (Asparouhov & Muthén, 2014), has become an effective alternative. The alignment evaluates measurement invariance and more importantly, permits factor mean comparisons without requiring scalar invariance which is usually required in traditional multiple-group CFA. Some simulation studies and empirical studies have investigated the applicability of alignment under different conditions, but some areas remain unexplored. Based on the simulation studies of Asparouhov and Muthén and of Flake and McCoach, this current simulation study is broken into three parts. The first and second parts investigate the acceptable noninvariance rates and minimal group sizes required for alignment in three factor models. The third part compares the performance of multiple-group CFA, multiple-group ESEM, and alignment by including different proportions and magnitudes of cross-loadings in the models. Results show that multiple-group CFA provides accurate factor mean estimates only when each factor had 20% factor loading (1 factor loading) with small-sized cross-loading. Multiple-group ESEM provides accurate factor mean estimates when the magnitude of cross-loading is small or when each factor had 20% factor loading (1 factor loading) with medium-sized cross-loading. Alignment provides accurate factor mean estimates when there are only small-sized cross-loadings in the model. The parameter estimates, coverage rates and ratios of average standard error to standard deviation for each method are not influenced by varying the amount of groups. Recommendations are included for using multiple-group CFA, multiple-group ESEM, and alignment based on the results.