A collection of algorithms and data structures are presented which provide incremental dispatch table modification. Incrementally modified dispatch tables allow table-based dispatch techniques to be used in reflective, dynamically typed, single-receiver languages with type/implementation-paired multiple inheritance. By storing a small amountof information, the algorithms can incrementally maintain the entire dispatch environment during the four fundamental environment modification requests: adding/removing selectors to/from classes and adding/removing class hierarchy links. The algorithms combine method dispatch calculation, inheritance management, and inheritance conflict detection into a single process, making the algorithms highly efficient. The algorithms also incrementally compute hierarchy information useful during compilation to establish which method addresses can be uniquely identified during compilation.