  The beginning of the cosmological phase bearing the direct kinematic imprints
of supernovae dimming may significantly vary within different models of
late-time cosmology, even if such models are able to fit present SNe data at a
comparable level of statistical accuracy. This effect -- useful in principle to
discriminate among different physical interpretations of the
luminosity-redshift relation -- is illustrated here with a pedagogical example
based on the LTB geometry.
