  The method of analytic continuation is used to find exact integral equations
for a selection of finite-volume energy levels for the non-unitary minimal
models $M_{2,2N+3}$ perturbed by their $\varphi_{13}$ operators. The N=2 case
is studied in particular detail. Along the way, we find a number of general
results which should be relevant to the study of excited states in other
models.
