  We discuss the principles governing the selection of inflationary models for
which preheating can affect the CMB. This is a (fairly small) subset of those
models which have non-negligible entropy/isocurvature perturbations on large
scales during inflation. We study new models which belong to this class -
two-field inflation with negative nonminimal coupling and
hybrid/double/supernatural inflation models where the tachyonic growth of
entropy perturbations can lead to the variation of the curvature perturbation,
${\cal R}$, on super-Hubble scales. Finally we present evidence against recent
claims for the variation of ${\cal R}$ in the absence of substantial
super-Hubble entropy perturbations.
