Data-intensive applications benefit from an intrinsic data parallelism that should be exploited on parallel systems to lower execution time. In the last years, data grids have been developed to handle, process, and analyze the tremendous amount of data produced in many scientific areas. Although very large, these grid infrastructures are under heavy use and efficiency is of utmost importance. This paper deals with the optimization of workflow managers used for deploying complex data-driven applications on grids. In that kind of application, we show how to better exploit data parallelism than currently done in most existing workflow managers. We present the design of a prototype implementing our solution and we show that it provides a significant speed-up w.r.t existing solutions by exemplifying results on a realistic medical imaging application.