  The phase behaviour of a weakly polydisperse system, such as a colloid with a
small spread of particle sizes, can be related perturbatively to that of its
monodisperse counterpart. I show how this approach can be generalized to remain
well-behaved near critical points, avoiding the divergences of existing methods
and giving access to some of the key qualitative features of polydisperse phase
equilibria. The analysis explains also why in purely size polydisperse systems
the critical point is, unusually, located very near the maximum of the cloud
and shadow curves.
