Triplet extensions are attractive alternatives to the standard model (SM) of particle physics. While models with only one triplet are highly constrained by electroweak precision observables, this is not necessarily the case once several triplets are present as in the Georgi-Machacek model. As in all other BSM models, the parameter space of triplet extensions is constrained by the condition that perturbative unitarity is not violated. For this purpose, limits on the eigenvalues of the scalar 2→2 scattering matrix are set. It is very common in the BSM literature that the scattering matrix is calculated under one crucial assumption: the scattering energy s is so large that only point interactions involving quartic couplings provide non-negligible contributions. However, it is not given that this approximation is always valid—in fact, diagrams involving propagators can play an important role. We discuss the examples of (i) the SM model extended by a real triplet, (ii) the Y=1 triplet extension of the SM, and (iii) the Georgi-Machacek model, how the tree-level unitarity constraints are affected once the large s approximation is given up. For all models we find that the impact of (effective) cubic couplings can be crucial.