This thesis presents an investigation of two new techniques for eliminating redundancy inherent in uses of dynamic polymorphism operations such as virtual dispatches and type tests. The novelty of both approaches derives from taking a subject-oriented perspective which considers multiple applications to the same run-time values, as opposed to previous site-oriented reductions which treat each operation independently. The first optimization (redundant polymorphism elimination -- RPE) targets reuse over intraprocedural contexts, while the second (instance-specializing polymorphism elimination -- ISPE) considers repeated uses of the same fields over the lifetime of individual object and class instances. In both cases, the specific formulations of the techniques are guided by a study of intentionally polymorphic constructions as seen in applications of common object-oriented design patterns. The techniques are implemented in Jikes RVM for the dynamic polymorphism operations supported by the Java programming language, namely virtual and interface dispatching, type tests, and type casts. In studying the complexities of Jikes RVM's adaptive optimization system and run-time environment, an improved evaluation methodology is derived for characterizing the performance of adaptive just-in-time compilation strategies. This methodology is applied to demonstrate that the proposed optimization techniques yield several significant improvements when applied to the DaCapo benchmarks. Moreover, dramatic improvements are observed for two programs designed to highlight the costs of redundant polymorphism. In the case of the intraprocedural RPE technique, a speed up of 14% is obtained for a program designed to focus on the costs of polymorphism in applications of the Iterator pattern. For the instance-specific technique, an improvement of 29% is obtained for a program designed to focus on the costs inherent in constructions similar to the Decorator pattern. Further analyses also point to several ways in which the results of this work may be used to complement and extend existing optimization techniques, and provide clarification regarding the role of polymorphism in object-oriented design.