The method of analytic continuation is used to find exact integral equ
ations for a selection of finite-volume energy levels for the non-unit
ary minimal models M-2,M-2N+3 perturbed by their phi(13) operators. Th
e 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 ex
cited states in other models. (C) 1998 Elsevier Science B.V.