A new technique is presented in this paper to improve the efficiency of data scheduling for multi-context reconfigurable architectures targeting multimedia and DSP applications. The main goal is to improve the applications execution time minimizing external memory transfers. Some amount of on-chip data storage is assumed to be available in the reconfigurable architecture. Therefore the Complete Data Scheduler tries to optimally exploit this storage, saving data and result transfers between on-chip and external memories. In order to do this, specific algorithms for data placement and replacement have been designed. We also show that a suitable data scheduling could decrease the number of transfers required to implement the dynamic reconfiguration of the system.