  Using modern nucleon-nucleon interactions in the description of the $A=3,4$
nuclear systems the $\chi^2$ per datum results to be much bigger than one. In
particular it is not possible to reproduce the three- and four-nucleon binding
energies and the $n-d$ scattering length simultaneously. This is one
manifestation of the necessity of including a three-nucleon force in the
nuclear Hamiltonian. In this paper we perform an analysis of some, widely used,
three-nucleon force models. We analyze their capability to describe the
aforementioned quantities and, to improve their description, we propose
modifications in the parametrization of the models. The effects of these new
parametrization are studied in some polarization observables at low energies.
