Support for complex data in object-relational database systems is based on abstract data types (ADTs). We argue that the current ADT approach inhibits the performance of queries that involve expensive operations on data types. Instead, we propose the Enhanced Abstract Data Type (E-ADT) paradigm, which treats operations on data types as declarative expressions that can be optimized. In this paper, we describe the E-ADT paradigm and PREDATOR, an object-relational database system based on E-ADTs. An E-ADT is an abstract data type enhanced with query optimization. Not only does an E-ADT provide operations (or methods) that can be used in SQL queries, it also supports internal interfaces that can be invoked to optimize these operations. This added functionality is provided without compromising the modularity of data types and the extensibility of the type system. Building such a database system requires fundamental changes in the architecture of the query processing engine; we present the system-level interfaces of PREDATOR that support E-ADTs, and describe the internal design details. Initial performance results from supporting image, time-series, and audio data as E-ADTs demonstrate an order of magnitude in performance improvements over the current ADT approach. Further, we describe how the E-ADT paradigm enables future research that can improve several aspects of object-relational query optimization. Consequently, we make the case that next-generation object-relational database systems should be based on E-ADT technology.