In the midst of the current biodiversity crisis, conservation efforts might profitably be directed towards ensuring that extinctions do not result in inordinate losses of evolutionary history. Numerous methods have been developed to evaluate the importance of species based on their contribution to total phylogenetic diversity on trees and networks, but existing methods fail to take complementarity into account, and thus cannot identify the best order or subset of taxa to protect. Here, we develop a novel iterative calculation of the heightened evolutionary distinctiveness and globally endangered metric (I-HEDGE) that produces the optimal ranked list for conservation prioritization, taking into account complementarity and based on both phylogenetic diversity and extinction probability. We applied this metric to a phylogenetic network based on mitochondrial control region data from extant and recently extinct giant Galápagos tortoises, a highly endangered group of closely related species. We found that the restoration of two extinct species (a project currently underway) will contribute the greatest gain in phylogenetic diversity, and present an ordered list of rankings that is the optimum complementarity set for conservation prioritization.