The Constant Bandwidth Server (CBS) is an effective scheduling technique frequently used to handle overruns and implement resource reservation in real-time systems where tasks have variable execution requirements. The behavior of the server is tuned by two parameters: the server bandwidth, which defines the fraction of the processor allocated to the task, and the server period, which defines the time granularity of the allocation. The effect of the granularity on task executions has never been studied before, so it is typically assigned using ad-hoc considerations. This paper presents a statistical study to evaluate the effects of the server parameters on task response times, and proposes a technique to compute the best parameters that minimize the average response time of the served tasks.