  We propose a more general version of the Trans-Planckian Censorship
Conjecture (TCC) which can apply to models of inflation with varying speed of
sound. We find that inflation models with $c_S < 1$ are in general more
strongly constrained by censorship of trans-Planckian modes than canonical
inflation models, with the upper bound on the tensor/scalar ratio reduced by as
much as three orders of magnitude for sound speeds consistent with bounds from
data. In particular, models which satisfy the TCC, and therefore the de Sitter
Swampland Conjecture, can still violate the more general condition for
non-classicality of trans-Planckian modes. As a concrete example, we apply the
constraint to Dirac-Born-Infeld inflation models motivated by string theory.
