A supertree is a phylogeny formed by combining information from disparate phylogenetic trees. Supertree methods have been particularly used for constructing large phylogenies from previously published trees and there is a growing literature using supertree methods for phylogenetic inference in macroevolutionary studies (e.g., Davies et al., 2004; Grotkopp et al., 2004; Salamin and Davies, 2004). This empirical supertree work has mostly used matrix representation with parsimony (standard MRP; Baum, 1992; Ragan, 1992) in which optimal supertrees are found by parsimony analysis of a matrix encoding the full splits of the input trees. A major concern with standard MRP (and some other) supertrees is that they can display relationships that seem to lack evidential support from the input trees, either individually or jointly (Bininda-Emonds and Bryant, 1998; Pisani and Wilkinson, 2002; Wilkinson et al., 2004b). This has prompted the development of measures of support that attempt to distinguish supported and unsupported relationships in supertrees (Bininda-Emonds, 2003; Wilkinson et al., 2005b). A standard means of analyzing the distribution of support across a phylogenetic hypothesis is to deconstruct a tree into the less complex relationships that the tree entails. For example, bootstrap proportions are typically reported for a set of full splits (clades on rooted trees) on the taxa of interest, and a number of other measures on trees are focused at identifying clade-based support (e.g., Bremer, 1994; Larget and Simon, 1999). In the supetree context, clades must be supported by input trees rather than by characters, and a supertree and the input trees generally have different leaf sets, so that a supertree clade may not be displayed by any input tree. This has left scope for ambiguity as to how to identify and quantify support in the supertree context (Bininda-Emonds, 2003; Wilkinson et al., 2005b). One solution is to seek some kind of soft, or reduced, support, in which input clades that are compatible with or entailed by supertree clades are seen as providing some level of support for these supertree relationships. Previous work has two important limitations. It focuses only on support (or lack of support) for supertree clades (components, full splits), ignoring support for less inclusive relationships like partial splits, triplets, or nestings (Wilkinson, 1994). We show that a more sensitive measure of support, focusing on lower-level relationships, may give a different picture of which supertree relationships are supported and unsupported. In fact, a supertree clade can appear unsupported despite all the triplets it implies being supported. As noted by Wilkinson et al. (2005b), “input trees may jointly entail, and thus strictly support, novel relationships that are not strictly supported by any single input tree.” The second limitation of previous work is that it relies on pairwise comparisons between each input tree and the supertree and consequently does not fully account for support jointly entailed by combinations of input trees. As the primary use of supertree methods is to combine information from a set of input trees, being able to identify this kind of support seems particularly important. Some authors have claimed total-evidence-like properties of signal enhancement for supertree methods (Bininda-Emonds et al., 1999), but novel relationships displayed by a supertree (relationships not present on any of the input trees) are worrying if they are not implied by combinations of the input trees (see Pisani and Wilkinson, 2002). Focusing exclusively on a rooted supertree and rooted input trees, we present a method for examining the support for triplets in a rooted supertree that can be naturally extended to identify combined support for supertree relationships, based on inference rules for triplets. We show that considering this combined support can reveal support for additional supertree relationships and so better diagnose unsupported relationships.