The topological pressure is obtained as the leading zero of a dynamical zeta function. We consider the problem of computing this zero when it is close to a singularity. In particular we study a family of intermittent maps, which we argue exhibit a branch point singularity in its zeta functions. The convergence of the cycle expansion close to this point is extremely slow. To deal with this problem we consider a resummation of the cycle expansion. The idea is quite similar to that of Padé approximants, but the ansatz is a generalized series expansion around the branch point rather than a rational function. The improvement on convergence of the leading zero is considerable. We also briefly discuss the relation between correlation decay and the nature of the branch point.