Tests for incongruence as an indicator of among data partition conflict have played an important role in conditional data combination. When such tests reveal significant incongruence, this has been interpreted as rationale for not combining data in a single phylogenetic analysis. In this study of lorisiform phylogeny, we employ the incongruence length difference (ILD) test to assess conflict among three independent data sets. A large morphological data set and two unlinked molecular data sets, the mitochondrial cytochrome b gene and the nuclear interphotoreceptor retinoid binding protein (exon 1), are analyzed with various optimality criteria and weighting mechanisms in order to determine the phylogenetic relationships among slow lorises (Primates, Loridae). When analyzed separately, the morphological data show impressive statistical support for a monophyletic Loridae. Both molecular data sets resolve the Loridae as paraphyletic, though with different branching order depending on optimality criterion and/or character weighting employed. When the three data partitions are analyzed in various combinations, an inverse relationship between congruence and phylogenetic accuracy is observed. Nearly all combined analyses that recover monophyly indicate strong data partition incongruence (p = 0.00005, in the most extreme case) whereas all analyses that recover paraphyly indicate lack of significant incongruence. Numerous lines of evidence verify that monophyly is the accurate phylogenetic result. Therefore, this study contributes to a growing body of information that affirms that measures of incongruence should not be employed as indicators of data set combinability.