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Incorporating auxiliary variables can potentially improve parameter estimate accuracy and efficiency when data have missingness. One common practice to select auxiliary variables, when many variables exist, is to keep those correlating the highest with the variables of research interest. In structural equation modeling, little is known about the influence of auxiliary variables when they correlates high with latent factors, but low with measurement indicators. By using computer-generated data, the authors showed that auxiliary variables correlating high with latent factors improve parameter estimate accuracy, controlling the correlation between auxiliary variables and observed indicators at a lower level (e.g., .2). Therefore researchers should be careful not to miss any auxiliary variables which have relatively small correlation with observed measurement indicators.