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The success of the cloud computing paradigm is due to its on-demand, self-service, and pay-by-use nature. According to this paradigm, the effects of Denial of Service (DoS) attacks involve not only the quality of the delivered service, but also the service maintenance costs in terms of resource consumption. Specifically, the longer the detection delay is, the higher the costs to be incurred. Therefore, a particular attention has to be paid for stealthy DoS attacks. They aim at minimizing their visibility, and at the same time, they can be as harmful as the brute-force attacks. They are sophisticated attacks tailored to leverage the worst-case performance of the target system through specific periodic, pulsing, and low-rate traffic patterns. In this paper, we propose a strategy to orchestrate stealthy attack patterns, which exhibit a slowly-increasing-intensity trend designed to inflict the maximum financial cost to the cloud customer, while respecting the job size and the service arrival rate imposed by the detection mechanisms. We describe both how to apply the proposed strategy, and its effects on the target system deployed in the cloud.