This paper presents PIPQ, a strict and linearizable concurrent priority queue whose design differs from existing solutions in literature because it focuses on enabling parallelism of insert operations as opposed to accelerating delete-min operations, as traditionally done. In a nutshell, PIPQ's structure includes two levels: the worker level and the leader level. The worker level provides per-thread data structures enabling fast and parallel insertions. The leader level contains the highest priority elements in the priority queue and can thus serve delete-min operations. Our evaluation, which includes an exploration of different data access patterns, operation mixes, runtime settings, and an integration into a graph-based application, shows that PIPQ outperforms competitors in a variety of cases, especially with insert-dominant workloads.