The aim of this article is to explore and critique recent aspirations to bridge the traditional divide between subjective and objective accounts of wellbeing through a psychological concordance thesis, according to which flourishing and happiness will, for psychological reasons, go hand in hand. Two varieties of the concordance thesis are explored, one psychological in origin and the other philosophical, with a special focus on the latter (derived from Aristotle) as it makes more radical psychological claims. Counterexamples are provided and discussed of unhappy and not-happy-enough flourishers, and of happy and not-unhappy-enough non-flourishers. The implications of those counterexamples are elicited, with the conclusion being that normative claims about the relative priority of flourishing over happiness (or vice versa) for wellbeing cannot be avoided with impunity. The concordance thesis does not seem to bear scrutiny, at least not as a thesis about ‘psychological necessity’; however, this leaves both a less demanding ‘rule-of-thumb’ concordance thesis, and a host of complementary theses about flourishing and happiness, intact.