Although a variety of supertree methods has been proposed, our understanding of these methods is limited. In turn, this limits the potential for biologists who seek to construct supertrees to make informed choices among the available methods. In this chapter we distinguish between supertree methods that offer a conservative synthesis of the relationships that are agreed upon or uncontradicted by all the input trees and liberal supertree methods which have the potential to resolve conflict. We list a series of potential desiderata (i.e.desirable properties) of liberal supertree methods, discuss their relevance to biologists and highlight where it is known that particular methods do or do not satisfy them. For biologists, the primary aim of liberal supertree construction is to produce accurate phylogenies and most of our desiderata relate to this prime objective. Secondary desiderata pertain to the practicality of supertree methods, particularly their speed.