  Tensor modes in the cosmic microwave background are one of the most robust
signatures of inflation. We derive theoretical bounds on the tensor fraction,
as a generalization of the well-known Lyth bound. Under reasonable assumptions,
the new bounds are at least two orders of magnitude stronger than the original
one. We comment on a previously derived generalization, the so-called
Efstathiou-Mack relationship. We also derive a new absolute upper bound on
tensors using de Sitter entropy bounds.
