[U]niversals or tropes are credible only if they are sparse. It is quite easy to believe that a point particle divides into a few non-spatiotemporal parts in such a way that one of them gives the particle its charge, another gives it its mass, and so on. But it is just absurd to think that a thing has (recurring or non-recurring) non-spatiotemporal parts for all its countless abundant properties! And it is little better to think that a thing has a different non-spatiotemporal part for each one of its properties that we might ever mention or quantify over.
-- David Lewis, On the Plurality of Worlds, pp.66-67.
The sparse properties are those "perfectly natural" properties which a completed physics could uncover. They "carve [nature] at the joints" (p.60). These could plausibly be fundamental constitutents of reality. Not so for the "abundant" properties, however. Those are better understood as nominalistic constructions, perhaps as the sets of all their instances (across all possible worlds). Lewis suggests (p.56) that this construction captures one conception of the 'property' role, but for those that want to distinguish necessarily co-extensive properties (e.g. triangularity and trilaterality), we can also construct structured properties to satisfy them.
Pretty cool, really. I'm happy with the idea of sparse tropes and constructed abundant properties. Seems sensible enough, which is more than can be said of the alternatives I'd previously come across!