Dynamic capacity provisioning is a useful technique for handling the multi-time-scale variations seen in Internet workloads. In this paper, we propose a novel dynamic provisioning technique for multi-tier Internet applications that employs (i) a flexible queuing model to determine how much resources to allocate to each tier of the application, and (ii) a combination of predictive and reactive methods that determine when to provision these resources, both at large and small time scales. Our experiments on a forty-machine Linuxbased hosting platform demonstrate the responsiveness of our technique in handling dynamic workloads. In one scenario where a flash crowd caused the workload of a three-tier application to double, our technique was able to double the application capacity within five minutes, thus maintaining response time targets.