This paper explores the benefits of scheduling off-chip memory operations in a Chip Multiprocessor (CMP) according to their execution relevance. Assuming the scenario of having many out-of-order execution cores in the CMP, from the processor perspective, the importance of the instruction that triggers an access to off-chip memory may vary considerably. Consequently, it makes sense to consider this point of view at the memory controller level to reorder outgoing memory accesses. After exploring different processor-centric sorting criteria, we reach the conclusion that the most simple and useful metric for scheduling a memory operation is the position in the reorder buffer of the instruction that triggers the on-chip miss. We propose a simple memory controller scheduling policy that employs this information as its main parameter. This proposal significantly improves system responsiveness, both in terms of throughput and fairness. The idea is analyzed through full-system simulation, running a broad set of workloads with diverse memory behavior. When it is compared with other scheduling algorithms with similar complexity, throughput can be improved by an average of 10% and fairness enhanced by an average of 15% even in very adverse usage scenarios. Moreover, the idea supports the possibility of dynamically favoring throughput or fairness, according to the end-user requirements.