Storage requests are divided into high-priority requests generally requiring low response time and low-priority requests generally requiring high throughput. The high-priority requests are further divided into several priorities reflecting different classes of service. The low-priority requests are placed on a low-priority request queue where they are executed in a throughput-optimizing order generally different from their arrival order. For each high-priority request, if there are not more than a predetermined number n (e.g., 1) outstanding requests for execution by the disk drive of greater priority, then the request is placed on a high-priority request queue where it is generally executed ahead of requests on the low-priority request queue. If there are more than n such greater-priority requests outstanding, then the high-priority request is placed on the low priority request queue and included in the throughput optimization along with the low-priority requests. The number of priority levels for the high priority requests may be two or more, and in one illustrated embodiment is equal to three.