We introduced a general approach for computing tree leaf distances by inferring topologies and internal branch lengths for quartets of leaves. We used our novel anchoring to design DISTIQUE, a new statistically consistent summary method for species tree estimation. DISTIQUE has variants, with several strategies for choosing and combining anchors. The default version of DISTIQUE requires O(n 3 k) running time and is much faster than ASTRAL. In terms of accuracy, DISTIQUE was nearly as accurate as ASTRAL with differences that were rarely substantial.