Heap-based priority queues are very common dynamical data structures used in several fields, ranging from operating systems to scientific applications. However, the rise of new multicore CPUs introduced new challenges in the process of design of these data structures: in addition to traditional requirements like correctness and progress, the scalability is of paramount importance. It is a common opinion that these two demands are partially in conflict each other, so that in these computational environments it is necessary to relax the requirements of correctness and linearizability to achieve high performances. In this paper we introduce a loosely coordinated approach for the management of heap based priority queues on multicore CPUs, with the aim to realize a tradeoff between efficiency and sequential correctness. The approach is based on a sharing of information among only a small number of cores, so that to improve performance without completely losing the features of the data structure. The results obtained on a scientific problem show significant benefits both in terms of parallel efficiency, as well as in term of numerical accuracy.