Lakatos argued that Carnap’s research programme in inductive logic was degenerative because it underwent a degenerative problem-shift by dealing with ever more specific internal problems and thereby moving further and further away from its original goals. Here I show that this criticism (which may apply to Carnap) cannot be levelled at the contemporary successor to Carnap’s programme, Bayesianism. To this end, I discuss various challenges and show how they can be addressed within the Bayesian research programme. In each of these cases, I argue, one can speak of a ‘progressive problem shift’. I therefore conclude that the Bayesian research programme in the methodology of science is progressive. Nevertheless, it is essential to continue to explore alternatives to it and to develop criteria for comparing competing research programmes.