  We analyse models of inflation in which isocurvature perturbations present
during inflation are converted into the primordial curvature perturbation
during instant preheating. This can be due to an asymmetry between the fields
present either during inflation or during preheating. We consider all the
constraints that the model must satisfy in order to be theoretically valid and
to satisfy observations. We show that the constraints are very tight in all of
the models proposed and special initial conditions are required for the models
to work. In the case where the symmetry is strongly broken during inflation the
non-Gaussianity parameter f_NL is generally large and negative.
