Summary Cloud providers (CPs) rely on server consolidation (the allocation of several virtual machines [VMs] on the same physical server) to minimize their costs. Maximizing the consolidation level is thus become 1 of the major goals of cloud providers. This is a challenging task because it requires the ability of estimating, in a resource contention scenario, multidimensional resource demands for multitier cloud applications that must meet service-level agreements (SLAs) in face of nonstationary workloads. In this paper, we cope with the problem of jointly allocating CPU and memory capacity to (a) precisely estimate their capacity required by each VM to meet its SLAs and (b) coordinate their allocation to limit the negative effects due to the interactions of dynamic allocation mechanisms, which, if ignored, can lead to SLA violations. We tackle this problem by devising FCMS, a feedback fuzzy controller that is able to dynamically adjust the CPU and memory capacity allocated to each VM in a coordinated way, to precisely match the needs induced by the incoming workload. By means of an extensive experimental evaluation, we show that FCMS is able to achieve the above goals and works better than existing state-of-the-art alternative solution in all the considered experimental scenarios.