Tasking in OpenMP 3.0 has been conceived to handle the dynamic generation of unstructured parallelism. New directives have been added allowing the user to identify units of independent work (tasks) and to define points to wait for the completion of tasks (task barriers). In this document we propose extensions to allow the runtime detection of dependencies between generated tasks, broading the range of applications that can benefit from tasking or improving the performance when load balancing or locality are critical issues for performance. The proposed extensions are evaluated on a SGI Altix multiprocessor architecture using a couple of small applications and a prototype runtime system implementation.