This paper introduces a novel admission test for partitioned CBS reservations on multi-core systems, that, on a new reservation arrival, is capable of exploiting better the CPU capacity in cases in which tasks have just recently left the CPU (for example, due to termination or migration to a different CPU). This is particularly useful for highly dynamic scenarios (with frequent arrivals of new tasks or leaves of existing ones) or when adaptive and possibly power-aware partitioning techniques (in which task migrations are triggered quite often to re-balance the workload among the available cores) are used