Dynamically reconfigurable hardware provides useful means to reduce the time-to-prototype and even the time-to-market in product designs. It also offers a good alternative in reconfiguring hardware logics to optimize the system performance. This paper targets an essential issue in reconfigurable computing, i.e., the minimization of configuration contexts. We explore different constraints on the CONTEXT MIN-IMIZATION problem. When the resulting subproblems are polynomial-time solvable, optimal algorithms are presented. We also present a greedy algorithm for the CONTEXT MINIMIZATION problem, that is proved N P-complete. The capability of the proposed algorithm is evaluated by a series of experiments.