Efficient message-passing implementations of shared data types are a vital component of practical distributed systems, enabling them to work on shared data in predictable ways, but there is a long history of results showing that many of the most useful types of access to shared data are necessarily slow. A variety of approaches attempt to circumvent these bounds, notably weakening consistency guarantees and relaxing the sequential specification of the provided data type. These trade behavioral guarantees for performance. We focus on relaxing the sequential specification of a first-in, first-out queue type, which has been shown to allow faster linearizable implementations than are possible for unrelaxed queues. The algorithms which showed these improvements in operation time tracked a complete execution history, storing complete object state at all n processes in the system, leading to n copies of every stored data element. In this paper, we consider the question of reducing the space complexity of linearizable implementations of shared data types, which provide intuitive behavior through strong consistency guarantees. We improve the existing algorithm for a relaxed queue, showing that it is possible to store only one copy of each element in a shared queue, while still having a low amortized time cost. This is one of several important steps towards making these data types practical in real world systems.