  The absolute V light curves of 5 SNe Ia, selected to represent the known
range of absolute luminosities at maximum for this class of objects, are
presented. Comparison of the long term luminosity evolution shows that the
differences seen at maximum persist, and actually increase with time,
einforcing the notion that intrinsic differences do exist among SNe Ia. Since
such differences are not accounted for in the standard progenitor scenario, it
becomes important to derive constraints for the models directly from the
observations. In order to investigate the influence of the two most important
parameters, that is the masses of the synthesized radioactive material and of
the ejecta, a simple MC light curve model was used to simulate the luminosity
evolution from the explosion to very late epochs (~1000 days). It was found
that the observations require a range of a factor 10 in the masses of the
radioactive material synthesized in the explosion (Mni= 0.1-1.1 Msun,) and a
factor 2 in the total mass of the ejecta (Mej = 0.7-1.4 Msun). Differences of a
factor 2 in Mni seem to be present even among `normal' SNe Ia. Some evidence
was also found that the deposition of the positrons from Co decay varies from
object to object, and with time. In particular, the latest HST observations of
SN 1992A seem to imply complete trapping of the positrons.
