  Recent results on the non-universality of the Initial Mass Function (IMF)
have shown strong evidence of IMF variations with galaxy velocity dispersion,
with a corresponding impact on other stellar population parameters, line
indices and colours. Using a set of stellar population models with varying IMF
slopes, we provide additional caveats on the assumption of a universal IMF. The
present study shows that the derived star formation histories of early-type
galaxies vary significantly with the IMF slope. For instance, a steepening in
the slope of a single power-law IMF decreases substantially, by a factor of up
to four, the contribution of the old stellar populations to the total
light/mass. This trend is milder for a segmented-like IMF shape, where the
contribution of the very low mass stars is decreased. It is also shown that, by
tuning each IMF slope to its prescribed value according to each galaxy velocity
dispersion, a sample of early-type galaxies covering a range of masses yield
comparable star formation histories. On the one hand, a small contribution from
relatively young stellar populations appear in the star formation histories of
most massive elliptical galaxies when adopting a steep IMF. On the other hand,
we find that low mass early-type galaxies that look like genuinely young
objects with a standard IMF (i.e. ``baby elliptical galaxies``), turn out to be
older when a slightly flatter IMF is employed. In summary, the use of a
non-universal IMF, tuned according to the velocity dispersion of the galaxy,
seems to provide more consistent results.
