In this work, we study the problem of getting quasi-additive bounds for the Hamiltonian of the long range Ising model, when the two-body interaction term decays proportionally to 1d2−α, α∈(0,1). We revisit the paper by Cassandro et al. [J. Math. Phys. 46, 053305 (2005)] where they extend to the case α∈[0,ln3ln2−1) the result of the existence of a phase transition by using a Peierls argument given by Fröhlich and Spencer [Commun. Math. Phys. 84, 87–101 (1982)] for α=0. The main arguments of Cassandro et al. [J. Math. Phys. 46, 053305 (2005)] are based in a quasi-additive decomposition of the Hamiltonian in terms of hierarchical structures called triangles and contours, which are related to the original definition of contours introduced by Fröhlich and Spencer [Commun. Math. Phys. 84, 87–101 (1982)]. In this work, we study the existence of a quasi-additive decomposition of the Hamiltonian in terms of the contours defined in the work of Cassandro et al. [J. Math. Phys. 46, 053305 (2005)]. The most relevant result obtained is Theorem 4.3 where we show that there is a quasi-additive decomposition for the Hamiltonian in terms of contours when α∈[0,1) but not in terms of triangles. The fact that it cannot be a quasi-additive bound in terms of triangles lead to a very interesting maximization problem whose maximizer is related to a discrete Cantor set. As a consequence of the quasi-additive bounds, we prove that we can generalise the [Cassandro et al., J. Math. Phys. 46, 053305 (2005)] result, that is, a Peierls argument, to the whole interval α∈[0,1). We also state here the result of Cassandro et al. [Commun. Math. Phys. 327, 951–991 (2014)] about cluster expansions which implies that Theorem 2.4 that concerns interfaces and Theorem 2.5 that concerns n point truncated correlation functions in Cassandro et al. [Commun. Math. Phys. 327, 951–991 (2014)] are valid for all α∈[0,1) instead of only α∈[0,ln3ln2−1).