  In a nonrelativistic contact four-fermion model we show that simple
regularisation prescriptions together with a definite fine-tuning of the
cut-off-parameter dependence of ``bare'' quantities give the exact solutions
for the two-particle sector and Goldstone modes. Their correspondence with the
self-adjoint extension into Pontryagin space is established leading to
self-adjoint semi-bounded Hamiltonians in three-particle sectors as well.
Renormalized Faddeev equations for the bound states with Fredholm properties
are obtained and analysed.
