Abstract. The cosmological bootstrap is an approach to directly fix inflationary primordial correlators from symmetries and first principles, bypassing the usual in-in computation. Approximate scale invariance has always been an important ingredient of the bootstrap, but now we have extended this philosophy to models which break it, in particular those with oscillatory potentials. As a result, we have found all resonant bispectra coming from tree-level inflaton self-interactions at all orders in derivatives, without assuming any specificities of the model other than the small oscillations of its potential. On the practical side, these templates will be useful for the search of oscillatory features in the inflationary dynamics. On the conceptual side, we hope that our work opens the path towards extending the cosmological bootstrap to more general theories of inflation.