The primordial curvature perturbation zeta may be generated by some curvaton
field sigma, which is negligible during inflation and has more or less negligible interactions until it decays. In the current scenario, the curvaton starts to oscillate while its energy density rho_sigma is negligible. We explore the opposite scenario, in which rho_sigma drives a few e-folds of inflation before the oscillation begins. In this scenario for generating zeta it is exceptionally easy to solve the eta-problem; one just has to make the curvaton a string axion, with anomaly-mediated susy breaking which may soon be tested at the LHC. The observed spectral index n can be obtained with a potential V~phi^p for the first inflation; p = 1 or 2 is allowed by the current uncertainty in n but the improvement in accuracy promised by Planck may rule out p = 1. The predictions include (i) running n'= 0.0026 (0.0013) for p = 1 (2) that will probably be observed, (ii) non-gaussianity parameter fNL ~ −1 that may be observed, (iii) tensor fraction r is probably too small to ever observed.