An I/O address translation method for specifying relaxed ordering for I/O accesses are provided. With the apparatus and method, storage ordering (SO) bits are provided in an I/O address translation data structure, such as a page table or segment table. These SO bits define the order in which reads and/or writes initiated by an I/O device may be performed. These SO bits are combined with an ordering bit, e.g., the Relaxed Ordering Attribute bit of PCI Express, on the I/O interface. The weaker ordering indicated either in the I/O address translation data structure or in the I/O interface relaxed ordering bit is used to control the order in which I/O operations may be performed.