obtained from Figure \[fig3\].

It is worth stressing the difference with previous non-perturbative results stemming from the $C_{0}$ solution, where all different cases (with the notable exception of IV) were predicting a reduction of the phase coexistence region. While in the $C_{0}$ description we have provided a careful treatment of polydispersity at the expenses of accuracy of the exploited approximation, in the perturbative description of the PY solution, polydispersity is assumed to be small and hence one might suspect that solutions with large polydispersities cannot fit within this picture. On a balance, nevertheless, we would favour the latter rather than the former description. An almost correct representation of the one-component counterpart, is a necessary requirement to check the effect of polydispersity on it, and we are not aware of any physical or experimental system where the effects of polydispersity are so strong that they could not kept into account, at least at the simplest qualitative level, by the perturbative scheme proposed here. Along this line, some further proposals have been put forward in Ref. [@Fantoni06] to derive a phenomenological BMCSL-like approximation for SHS, which might be regarded as our ’best and simplest guess’ to the *exact* phase behavior of polydisperse 