  We study models of inflation with two scalar fields and non-canonical kinetic
terms, focusing on the case in which the curvature and isocurvature
perturbations are strongly coupled to each other. In the regime where a heavy
mode can be identified and integrated out, we clarify the passage from the full
two-field model to an effectively single-field description. However, the strong
coupling sets a new scale in the system, and affects the evolution of the
perturbations as well as the beginning of the regime of validity of the
effective field theory. In particular, the predictions of the model are
sensitive to the relative hierarchy between the coupling and the mass of the
heavy mode. As a result, observables are not given unambiguously in terms of
the parameters of an effectively single field model with non-trivial sound
speed. Finally, the requirement that the sound horizon crossing occurs within
the regime of validity of the effective theory leads to a lower bound on the
sound speed. Our analysis is done in an extremely simple toy model of slow-roll
inflation, which is chosen for its tractability, but is non-trivial enough to
illustrate the richness of the dynamics in non-canonical multi-field models.
