Uncertain information is commonplace in real-world data management scenarios. The ability to represent large sets of possible instances (worlds) while supporting efficient storage and processing is an important challenge in this context. The recent formalism of world-set decompositions (WSDs) provides a space-efficient representation for uncertain data that also supports scalable processing. WSDs are complete for finite world-sets in that they can represent any finite set of possible worlds. For possibly infinite world-sets, we show that a natural generalization of WSDs precisely captures the expressive power of c-tables. We then show that several important decision problems are efficiently solvable on WSDs while they are NP-hard on c-tables. Finally, we give a polynomial-time algorithm for factorizing WSDs, i.e. an efficient algorithm for minimizing such representations.