Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in form factor perturbation theory and in principle works to any order. The procedure is carried out in detail for double sine-Gordon theory, where the vacuum energy density and breather mass correction is evaluated at second order. The results agree with those obtained from the truncated conformal space approach. The regularization procedure can also be used to compute other spectral sums involving disconnected pieces of form factors such as those that occur e.g. in finite temperature correlators. ; Comment: 14 pages, no figures, LaTeX2e file, v2: typos corrected, references and discussion of further details added