  This is a sequel to a previous detailed study of quantum corrections to
cosmological correlations. It was found there that except in special cases
these corrections depend on the whole history of inflation, not just on the
behavior of fields at horizon exit. It is shown here that at least in
perturbation theory these corrections can nevertheless not be proportional to
positive powers of the Robertson--Walker scale factor, but only at most to
powers of its logarithm, and are therefore never large.
