Numerous multivariate robust measures of location have been proposed and many have been found to be unsatisfactory in terms of their small-sample efficiency. Several new measures of location have recently been derived, however, nothing is known about their small-sample efficiency or how they compare to the sample mean under normality. This research compared the efficiency for p = 2, 5, and 8 with sample sizes n = 20 and 50 for p-variate data. Although previous studies indicate that so-called skipped estimators are efficient, this study found that variations of this approach can perform poorly when n is small and p exceeds 5. One of the best estimators was found to be a skipped estimator where outliers detected by a projection method are eliminated. The TBS, OGK and RMBA estimators were included and; in some cases, they performed well, however, serious exceptions were identified suggesting that a skipped estimator based on a projection-type outlier detection method is preferable based on efficiency.