In this study, we propose an efficient two-phase heuristic policy, called an acceptance tolerance control policy, for Infrastructure as a Service (IaaS) cloud services that considers both the service provider and customer in terms of profit and satisfaction, respectively. Each time an IaaS cloud service is requested, this policy determines whether the service is accepted or rejected by calculating the potential for realizing the two performance objectives. Moreover, it uses acceptance tolerance to identify the possibility for error with the chosen decision while compensating for both future fluctuations in customer demand and error possibilities based on past decisions. We conducted a numerical experiment to verify the performance of the proposed policy using several actual IaaS cloud service specifications and comparing it with other heuristics.