A filtering method is introduced for solving the zero-range three-boson
problem. This scheme permits to solve the original Skorniakov Ter-Martirosian
integral equation for an arbitrary large Ultra-Violet cut-off and to avoid the
Thomas collapse of the three particles. The method is applied to a more general
zero-range model including a finite background two-body scattering length and
the effective range. A cross-over in the Efimov spectrum is found in such
systems and a specific regime emerges where Efimov states are long-lived
