In (Petrick and Bacchus 2002), a "knowledge-level" approach to planning under incomplete knowledge and sensing was presented. In comparison with alternate approaches based on representing sets of possible worlds, this higher-level representation is richer, but the inferences it supports are weaker. Nevertheless, because of its richer representation, it is able to solve problems that cannot be solved by alternate approaches. In this paper we examine a collection of new techniques for increasing both the representational and inferential power of the knowledge-level approach. These techniques have been fully implemented in the PKS (Planning with Knowledge and Sensing) planning system. Taken together they allow us to solve a range of new types of planning problems under incomplete knowledge and sensing.