Little research has examined factors influencing statistical power to detect the correct number of latent classes using latent profile analysis (LPA). This simulation study examined power related to inter-class distance between latent classes given true number of classes, sample size, and number of indicators. Seven model selection methods were evaluated. None had adequate power to select the correct number of classes with a small (Cohen's d = .2) or medium (d = .5) degree of separation. With a very large degree of separation (d = 1.5), the Lo-Mendell-Rubin test (LMR), adjusted LMR, bootstrap likelihood-ratio test, BIC, and sample-size adjusted BIC were good at selecting the correct number of classes. However, with a large degree of separation (d = .8), power depended on number of indicators and sample size. The AIC and entropy poorly selected the correct number of classes, regardless of degree of separation, number of indicators, or sample size.