FIFO queues are a fundamental data structure used in a wide range of applications. Concurrent FIFO queues allow multiple execution threads to access the queue simultaneously. Maintaining strict FIFO semantics in concurrent queues leads to low throughput due to high contention at the head and tail of the queue. By relaxing the FIFO semantics to allow some reordering of elements, it becomes possible to achieve much higher scalability. This work presents two orthogonal designs for relaxed concurrent FIFO queues, one derived from the MultiQueue and the other based on ring buffers. We evaluate both designs extensively on various micro-benchmarks and a breadth-first search application on large graphs. Both designs outperform state-of-the-art relaxed and strict FIFO queues, achieving higher throughput and better scalability.