Flow Theory is a rich, effective theory introduced in order to study real-time network protocols. It is based on discrete mathematics in which a flow of data is represented by an infinite sequence of numbers and is characterized by its upper bounds. Unfortunately up to now Flow Theory has used a traffic characterization that in some cases can be too loose, thus causing an inefficient network utilization. In this paper we enhance Flow Theory by providing it with a more accurate traffic characterization and with all the tools necessary to deal with it. As we will see, this enhancement provide a more accurate performance evaluation and thus better network utilization.