A Monte Carlo study was conducted to estimate the efficiency of and the relationship between five equations and the use of cross validation as methods for estimating shrinkage in multiple correlations. Two of the methods were intended to estimate shrinkage to population values and the other methods were intended to estimate shrinkage from sample to sample. Comparisons were made for the six methods with three levels of population multiple correlations, four different sample sizes, and three different degrees of multicollinearity (average correlations among the predictor variables). One hundred samples were drawn for each of the 48 conditions. The data showed no advantage for the cross-validation procedure in comparison to the other methods. The major purpose of the study was to check the differential effects of multicollinearity on shrinkage estimates; but it was found to have virtually no effect. This may have been an artifact of the method used to generate the data. Caution is recommended against over-generalization from artificially generated data. (The computer program is appended). (CTM)