  We consider non-canonical generalizations of two classes of simple
single-field inflation models. First, we study the non-canonical version of
"ultra-slow roll" inflation, which is a class of inflation models for which
quantum modes do not freeze at horizon crossing, but instead evolve rapidly on
superhorizon scales. Second, we consider the non-canonical generalization of
the simplest "chaotic" inflation scenario, with a potential dominated by a
quartic (mass) term for the inflaton. We find a class of related non-canonical
solutions with polynomial potentials, but with varying speed of sound. These
solutions are characterized by a constant field velocity, and we dub such
models {\it isokinetic} inflation. As in the canonical limit, isokinetic
inflation has a slightly red-tilted power spectrum, consistent with current
data. Unlike the canonical case, however, these models can have an arbitrarily
small tensor/scalar ratio. Of particular interest is that isokinetic inflation
is marked by a correlation between the tensor/scalar ratio and the amplitude of
non-Gaussianity such that parameter regimes with small tensor/scalar ratio have
{\it large} associated non-Gaussianity, which is a distinct observational
signature.
