Server consolidation in virtualized data centers introduces new challenges for resource management, capacity provisioning, and guaranteeing application quality of service (QoS). This paper presents Nested QoS, a formal model that specifies application QoS by a response time distribution based on the burstiness of the workload. The workload is adaptively decomposed into classes with different response time guarantees and scheduled using an Earliest Deadline First policy. A procedure for determining the decomposition parameters is developed, and empirical results showing the benefits of decomposition and adaptive parameter setting are presented.