  We extend previous classifications of inflationary models by means of their
behaviour at large-N, where N is the number of e-foldings. In addition to the
perturbative 1/N case, whose slow-roll parameters fall off as powers of 1/N, we
introduce the constant, non-perturbative and logarithmic classes. This covers
the large majority of inflationary models. Furthermore, we calculate the
running of the spectral tilt for all these classes. Remarkably, we find that
the tilt's runnings essentially cluster around the permil level. We comment on
the implications for future experiments.
