This paper tackles the problem of admitting real-time tasks onto a symmetric multi-processor platform, where a partitioned EDF-based scheduler is used. We propose to combine a well-known utilization-based test for the first-fit partitioning strategy, with a simple heuristic based on the number of tasks and exact knowledge of the utilization of the first few biggest tasks. This results in an effective and efficient test improving on the state of the art in terms of admitted tasks, as shown by extensive tests performed on task sets generated using the widely adopted randfixedsum algorithm.