Representing and reasoning with temporal information is an essential part of many tasks in AI such as scheduling, planning and natural language processing. Two influential frameworks for representing temporal information are interval algebra and point algebra [1], [8]. Given a knowledge-base consisting of temporal relations, the main reasoning problem is to determine whether this knowledge-base is satisfiable, i.e., there is a scenario which is consistent with the information provided. However, when a given set of temporal relations is unsatisfiable, no further reasoning is performed. We argue that many real world problems are inherently overconstrained, and that these problems must also be addressed. This paper investigates approaches for handling overconstrainedness in temporal reasoning. We adapt a well studied notion of partial satisfaction to define partial scenarios or optimal partial solutions. We propose two reasoning procedures for computing an optimal partial solution to a problem (or a complete solution if it exists).