The increasing spread of elastic Cloud services, together with the pay-as-you-go pricing model of Cloud computing, has led to the need of an elasticity controller. The controller automatically resizes an elastic service in response to changes in workload, in order to meet Service Level Objectives (SLOs) at a reduced cost. However, variable performance of Cloud Virtual Machines and nonlinearities in Cloud services, such as the diminishing reward of adding a service instance with increasing the scale, complicates the controller design. We present the design and evaluation of ElastMan, an elasticity controller for Cloud-based elastic key-value stores. ElastMan combines feedforward and feedback control. Feedforward control is used to respond to spikes in the workload by quickly resizing the service to meet SLOs at a minimal cost. Feedback control is used to correct modeling errors and to handle diurnal workload. To address nonlinearities, our design of ElastMan leverages the near-linear scalability of elastic Cloud services in order to build a scale-independent model of the service. We have implemented and evaluated ElastMan using the Voldemort key-value store running in an OpenStack Cloud environment. Our evaluation shows the feasibility and effectiveness of our approach to automation of Cloud service elasticity.