Evolution operates on whole genomes by operations that change the order and strandedness of genes within the genomes. This type of data presents new opportunities for discoveries about deep evolutionary rearrangement events. Several distance-based phylogenetic reconstruction methods have been proposed [12],[21],[19] that use neighbor joining (NJ) [16] with the expected breakpoint or inversion distances after k rearrangement events. In this paper we study the variance of the breakpoint and inversion distances. The result is combined with Weighbor [5], an improved version of NJ using the variance of true evolutionary distance estimators, to yield two new methods, Weighbor-IEBP and Weighbor-EDE. Experiments show the new methods have better accuracy than all previous distance-based methods, and are robust against model parameter misspecifications.