Abstract.  We analyze two models in which primordial inflation has non-standard features.  In the first model we study the evolution of a system in which the inflaton is slowed down by dissipation of energy into gauge bosons instead of the usual Hubble friction: in particular we study the conditions of the onset of such a scenario from a static field configuration and we briefly mention some difficulties of the treatment of perturbations.  In the second model we consider the case of a metastable vacuum which sources exponential inflation and we show that the presence of scalar-tensor gravity can induce a power-law expansion which allows successful tunneling.  We also analyze the case in which such a metastable vacuum might be in the Standard Model Higgs potential.