  Black hole formation may occur if the spectrum of the curvature perturbation
\zeta increases strongly as the scale decreases. As no such increase is
observed on cosmological scales, black hole formation requires strongly
positive running n' of the spectral index n, though the running might only kick
in below the `cosmological scales' probed by the CMB anisotropy and galaxy
surveys. A concrete and well-motivated way of producing this running is through
the running mass model of slow roll inflation. We obtain a new observational
bound n' < 0.026 on the running provided by this model, improving an earlier
result by a factor two. We also discuss black hole production in more general
scenarios. We show that the usual conditions \epsilon << 1 and |\eta| << 1 are
enough to derive the spectrum {\cal P}_{\zeta}(k), the introduction of higher
order parameters \xi^{2} etc. being optional.
