The crucial handover elements in wireless ATM networks are handover delay and handover efficiency. Since the research about the handover in wireless ATM has until now focused mainly on minimizing handover delay, the results have shown the inefficiency of network resources. In broadband wireless ATM networks, handover efficiency is critical to network capacity. In this paper, we propose a new handover scheme based on a partial path rerouting scheme called the delay limited best-fit backtracking scheme. The scheme searches for the crossover switch that limits handover delay and at the same time maximizes handover efficiency. It uses a new crossover switch searching method, which is an adaptive backtracking searching method that uses a best-fit search manner, to search for the optimal crossover switch that satisfies the given crossover switch condition. We evaluated the performance of proposed handover scheme, and show that the suggested scheme can improve handover efficiency more than other handover schemes.