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We discuss some properties of a model Hamiltonian for a system of threebosons interacting via zero-range forces in three dimensions. In order to avoidthe well known instability phenomenon, we consider the so-called Minlos-Faddeevregularization of such Hamiltonian, heuristically corresponding to theintroduction of a three-body repulsion. We review the main concerning resultsrecently obtained. In particular, starting from a suitable quadratic form $Q$,the self-adjoint and bounded from below Hamiltonian $\mathcal H$ can beconstructed provided that the strength $\gamma$ of the three-body force islarger than a threshold parameter $\gamma_c$. Moreover, we give an alternativeand much simpler proof of the above result whenever $\gamma > \gamma'_c$, with$\gamma'_c$ strictly larger than $\gamma_c$. Finally, we show that thethreshold value $\gamma_c$ is optimal, in the sense that the quadratic form $Q$is unbounded from below if $\gamma<\gamma_c$.

Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions