Eric Olson has argued, startlingly, that no coherent account can be given of the distinction made in the personal identity literature between ‘complex views’ and ‘simple views’. ‘We tell our students,’ he writes, ‘that accounts of personal identity over time fall into [these] two broad categories’. But ‘it is impossible to characterize this distinction in any satisfactory way. The debate has been systematically misdescribed’. I argue, first, that, for all Olson has said, a recent account by Noonan provides the coherent characterization he claims impossible. If so we have not been wrong all along in the way he says in what we have been telling our students. I then give an account of the distinction between the reductionist and non-reductionist positions which makes it different from the complex/simple distinction. The aim is to make clear sense of the notion of a not simple but non-reductionist position – which seems an eminently reasonable possibility and something it may also be useful to tell our students about.