Total Least Squares (TLS) or orthogonal regression is used to remedy attenuation bias in optimal fingerprinting regressions. Consistency properties in multivariate applications require strong assumptions about unobservable variance ratios. Monte Carlo analysis is used herein to examine coefficient biases when the explanatory variables are correlated and have heterogeneous error variances. Ordinary Least Squares (OLS) exhibits the expected attenuation bias patterns which vanish as the noise variances on the explanatory variable disappear. TLS is generally more biased than OLS except under homogeneous noise variances. When the explanatory variables are negatively correlated TLS imparts a large upward bias which gets worse as the noise variance on the explanatory variable gets smaller. In general without specific diagnostic information TLS should not be considered an improvement on OLS and can yield extremely biased coefficients.