The aim of this chapter is to explore and critique recent efforts to bridge the traditional divide between subjective (‘happiness’) and objective (‘flourishing’) accounts of well-being through a 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) because it makes more radical psychological claims and is more relevant to the themes of the present work. Counter-examples are provided and discussed of unhappy and not-happy-enough flourishers, and of happy and not-unhappy-enough non-flourishers. The implications of those counter-examples are explored, the conclusion being that normative claims about the relative priority of flourishing over happiness (or vice versa) for well-being 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 intact both a less demanding ‘rule-of-thumb’ concordance thesis, and a host of complementary theses about flourishing and happiness. The educational upshot of the chapter is that enhancing student well-being may have little, if anything, to do with lessons in making them ‘happy’.