The well-known problems of tuning and self-tuning of data management systems are amplified in the context of Cloud environments that promise self management along with properties like elasticity and scalability. The intricate criteria of Cloud storage systems such as their modular, distributed, and multi-layered architecture add to the complexity of the tuning and self-tuning process. In this paper, we provide an architecture for a self-tuning framework for Cloud data storage clusters. The framework consists of components to observe and model certain performance criteria and a decision model to adjust tuning parameters according to specified requirements. As part of its implementation, we provide an overview on benchmarking and performance modeling components along with experimental results.