We study the renormalisation group flows between minimal W models by means of a new set of nonlinear integral equations which provide access to the effective central charge of both unitary and nonunitary models. We show that the scaling function associated to the nonunitary models is a nonmonotonic function of the system size.1. A recent study of the renormalisation group flows between nonunitary minimal models revealed an unexpected behaviour for the groundstate energy E 0 (R), in that it was a nonmonotonic function of the system size R [1]. The nonmonotonicity was illustrated using the finite-size scaling function c eff (r), which up to the bulk term is proportional to the groundstate energywhere M is the so-called crossover scale (the mass in massive theories). As the system size goes to zero c eff (r) becomes the effective central chargeWe denote the actual central charge by c while ∆ 0 is the conformal dimension of the lowest primary field of the UV CFT. The effective central charge and the central charge of the unitary minimal models coincide, and according to Zamolodchikov's c-theorem [2] there exists a function c which is monotonic. However, apart from the UV and IR points at which c equals the central charge of the relevant CFT, it is not clear if there is any connection with E 0 (r). Nevertheless the groundstate energy of the unitary models is always monotonic. Analogously it had been thought that the groundstate energy of the nonunitary models would also be monotonic, but the results of [1] and [3-6] provide a number of counter examples. In this letter we study a further set of perturbed conformal field theories, demonstrating that c eff (r) behaves nonmonotonically for the majority of nonunitary models.We consider the minimal models W G p,q N based on one of the simply laced Lie algebras. The models are specified by two coprime integers p and q with p > h, in terms of which the central charge and the effective central charge are c = N 1 − h(h + 1)(p − q) 2 pq , c eff = N 1 − h(h+1) pq .