Formal analysis methods of embedded systems provide safe, but unfortunately often pessimistic bounds on response times. An important source of pessimism is the common approach to characterize service request either by the amount of data or the number of events to be processed. Several works, e.g. [1]-[4], have demonstrated that a dual model - which includes information on both data and events - is more accurate, especially for more complex scheduling problems. In this paper, we enrich Compositional Performance Analysis (CPA) by a new component interface which, as we show, is consistent with the generic dual model proposed in [3]. Furthermore, we discuss how composition of components should be realized and how the new information should be integrated into the analysis technique. The improved CPA is called CPA+, and we identify different types of scenarios where CPA+ is particularly beneficial.