Regression analysis is one of the more common analytic tools used by researchers. However, multicollinearity between the predictor variables can cause problems in using the results of regression analyses. Problems associated with multicollinearity include entanglement of relative influences of variables due to reduced precision of estimation, inappropriate dropping of variables from analysis, and oversensitivity of estimates of coefficients to particular sets of sample data. Alternative estimators have been developed that, when faced with severe multicollinearity, result in better estimates than do ordinary least squares (OLS) methods. However, little research has been conducted concerning the break-even point between OLS and other alternatives. The simulation presented in this article addresses this problem using regression that involves principal components. Data were generated for each of 72 experimental runs. Results indicate that the following three alternatives, differing on the criterion for selecting which components to use, appear to be reasonable: the Park criterion; the all but one criterion; and selection up to all but one based on correlation with the criterion variable. A 16-item list of references and 4 data tables are included. (TJH)