Due to its speed, the distance approach remains the best hope for building phylogenies on very large sets of taxa. Recently (R. Desper and O. Gascuel, J. Comp. Biol.9:687–705, 2002), we introduced a new ‘‘balanced’’ minimum evolution (BME) principle, based on a branch length estimation scheme of Y. Pauplin (J. Mol. Evol.51:41–47, 2000). Initial simulations suggested that FASTME, our program implementing the BME principle, was more accurate than or equivalent to all other distance methods we tested, with running time significantly faster than Neighbor-Joining (NJ). This article further explores the properties of the BME principle, and it explains and illustrates its impressive topological accuracy. We prove that the BME principle is a special case of the weighted least-squares approach, with biologically meaning fulvariances of the distance estimates. We show that the BME principle is statistically consistent. We demonstrate that FASTME only produces trees with positive branch lengths, a feature that separates this approach from NJ (and related methods) that may produce trees with branches with biologically meaning less negative lengths. Finally, we consider a large simulated data set, with 5,000 100-taxon trees generated by the Aldous beta-splitting distribution encom passing a range of distributions from Yule-Harding to uniform, and using a covarion-like model of sequence evolution. FASTMEproduces trees faster than NJ, and much faster than WEIGHBOR and the weighted least-squares implementation ofPAUP*. Moreover, FASTME trees are consistently more accurate at all settings, ranging from Yule-Harding to uniformdistributions, and all ranges of maximum pairwise divergence and departure from molecular clock. Interestingly, thecovarion parameter has little effect on the tree quality for any of the algorithms.