A digital system with an improved transaction ordering policy is disclosed. Individual occurrences of requests for access to common system resources specify whether or not the request is ordered. In some embodiments, the invention includes a memory that holds data, a controller, and at least two processors that generate requests to access the memory data. Each access request includes an indication of whether or not this request is to be performed in a sequential order among other access requests and, if so, an indication of the order. The controller receives the access requests from each processor, determines a performance order for the requests, and provides the access requests to the memory in the performance order. The performance order conforms to the specified order when the access requests so indicate.