  The young LMC cluster NGC 1866 represents the ideal laboratory for testing
stellar evolutionary models: in particular, it can be used to discriminate
among classical stellar models, in which the extension of the convective
regions is fixed by the classical Schwarzschild criterion, from models with
overshooting, in which an ``extra-mixing'' is considered to take place beyond
the classical limit of the convective zone. Addressing this subject in a recent
work, Testa et al. (1999) reached the conclusion that the classical scheme for
the treatment of convection represents a good and sufficient approximation for
convective interiors. Using their own data, we repeat here the analysis. First
we revise the procedure followed by Testa et al. (1999) to correct the data for
completeness, second we calculate new stellar models with updated physical
input for both evolutionary schemes, finally we present many simulations of the
colour-magnitude diagrams and luminosity functions of the cluster using the
ratio of the integrated luminosity function of main sequence stars to the
number of giants as the normalization factor of the simulations. We also take
into account several possible physical agents that could alter the
color-magnitude diagram and the luminosity function: they are unresolved binary
stars, dispersion in the age, stochastic effects in the initial mass function.
Their effect is analyzed separately, with the conclusion that binary stars have
the largest impact. The main result of this study is that the convective
overshoot hypothesis (together with a suitable percentage of unresolved
binaries) is really needed to fully match the whole pattern of data. The main
drawback of the classical models is that they cannot reproduce the correct
ratio of main sequence to post-main sequence stars.

Astrophysics