This article reconsiders the way metafrontiers and associated measures of efficiency are obtained from nonparametric estimates of underlying group-specific frontiers. Both convex and non-convex metasets have been applied, but the large majority of articles applying this popular methodology assume that the metafrontier envelops a convex metaset. We argue that associated estimates of efficiency are potentially unreliable. We develop a refined methodology for nonparametric envelopment of non-convex metasets. We apply our methodology to a secondary data set to illustrate the potential errors associated with the currently established methods. Anticipating our main conclusion, we find that the convexification strategy consisting in assuming a convex metaset generally leads to erroneous results.