Complete search algorithms are important methods for solving Distributed Constraint Optimization Problems (DCOPs), which generally utilize bounds to prune the search space. However, obtaining high-quality lower bounds is quite expensive since it requires each agent to collect more information aside from its local knowledge, which would cause tremendous traffic overheads. Instead of bothering for bounds, we propose a Bound-Independent Pruning (BIP) technique for existing tree-based complete search algorithms, which can independently reduce the search space only by exploiting local knowledge. Specifically, BIP enables each agent to determine a subspace containing the optimal solution only from its local constraints along with running contexts, which can be further exploited by any search strategies. Furthermore, we present an acceptability testing mechanism to tailor existing tree-based complete search algorithms to search the remaining space returned by BIP when they hold inconsistent contexts. Finally, we prove the correctness of our technique and the experimental results show that BIP can significantly speed up state-of-the-art tree-based complete search algorithms on various standard benchmarks.