  Using a correspondence between the spectrum of the damped wave equation and
non-self-adjoint Schroedinger operators, we derive various bounds on complex
eigenvalues of the former. In particular, we establish a sharp result that the
one-dimensional damped wave operator is similar to the undamped one provided
that the L^1 norm of the (possibly complex-valued) damping is less than 2. It
follows that these small dampings are spectrally undetectable.
