Tasks are a good support for composition. During the development of a high-level component model for HPC, we have experimented to manage parallelism from components using OpenMP tasks. Since version 4-0, the standard proposes a model with dependent tasks that seems very attractive because it enables the description of dependencies between tasks generated by different components without breaking maintainability constraints such as separation of concerns. The paper presents our feedback on using OpenMP in our context. We discover that our main issues are a too coarse task granularity for our expected performance on classical OpenMP runtimes, and a harmful task throttling heuristic counter-productive for our applications. We present a completion time breakdown of task management in the Intel OpenMP runtime and propose extensions evaluated on a testbed application coming from the Gysela application in plasma physics.