With steady improvement in the reliability and performance of communication devices, routing instabilities now contribute to many of the remaining service degradations and interruptions in modern networks. This has led to a renewed interest in centralized routing systems that, compared to distributed routing, can provide greater control over routing decisions and better visibility of the results. One benefit of centralized control is the opportunity to readily eliminate transient routing loops, which arise frequently after network changes because of inconsistent routing states across devices. Translating this conceptual simplicity into a solution with tolerable message complexity is non-trivial. Addressing this issue is the focus of this paper. We identify when and why avoiding transient loops might require a significant number of messages in a centralized routing system, and demonstrate that this is the case under many common failure scenarios. We also establish that minimizing the number of required messages is NP-hard, and propose a greedy heuristic that we show to perform well under many conditions. The paper's results can facilitate the deployment and evaluation of centralized architectures by leveraging their strengths without incurring unacceptable overhead.