We present a new, concurrent, lock-free priority queue that relaxes the delete-min operation to allow deletion of any of the ρ+1 smallest keys instead of only a minimal one, where ρ is a parameter that can be configured at runtime. It is built from a logarithmic number of sorted arrays, similar to log-structured merge-trees (LSM). For keys added and removed by the same thread the behavior is identical to a non-relaxed priority queue. We compare to state-ofthe-art lock-free priority queues with both relaxed and non-relaxed semantics, showing high performance and good scalability of our approach. Categories and Subject Descriptors E.1 [Data]: Data Structures— Distributed data structures Keywords Task-parallel programming, priority-queue, concurrent data structure relaxation, shared memory