Self-optimization through dynamic resource provisioning is an appealing approach to tackle load variation in Internet services. It allows to assign or release resources to/from Internet services according to the varying load. However, dynamic resource provisioning raises several challenges among which: (i) How to plan a good capacity of an Internet service, i.e.~a necessary and sufficient amount of resource to handle the Internet service workload, (ii) How to manage both gradual load variation and load peaks in Internet services, (iii) How to prevent system oscillations in presence of potentially concurrent dynamic resource provisioning, and (iv) How to provide generic self-optimization that applies to different Internet services such as e-mail services, streaming servers or e-commerce web systems. This paper precisely answers these questions. It presents the design principles and implementation details of a self-optimization autonomic manager. It describes the results of an experimental evaluation of the self-optimization manager with a realistic e-commerce multi-tier web application running in a Linux cluster of computers. The experimental results show the usefulness of self-optimization in terms of end-user's perceived performance and system's operational costs, with a negligible overhead.