DETECT is a nonparametric methodology to identify the dimensional structure underlying test data. The associated DETECT index, Dmax, denotes the degree of multidimensionality in data. Conditional covariances (CCOV) are the building blocks of this index. In specifying population CCOVs, the latent test composite θ TT is used as the conditional variable. In estimating the CCOVs, the total test score of all items in the test ( T) or the rest score of remaining items ( S) are generally used as estimates of the latent composite θ TT . However, estimated CCOVs are biased when using T or S as a proxy for θ TT. Some type of correction is needed to adjust this bias. This study was an investigation of different ways to estimate the DETECT index based on the conditional scores T and S, and additional bias adjustments, resulting in six different estimates, D1 through D6. These six indices were investigated in simulated settings, varying the test length, sample size, and the degree of multidimensionality (108 in all). The results showed that indices D1, D2, and D5 are not acceptable as they displayed highly inflated Dmax values. No statistically significant differences were found between indices D3 and D6. Overall comparison of indices D3 with D4 showed that even though they differed significantly in Dmax values, there was no practically meaningful difference between the performance of these two indices. For these reasons, it is recommended that the current index D3 be retained even though index D4 displayed slightly better results in the current study.