An apparatus includes a first circuit to determine a real program order (RPO) of an eldest undispatched instruction from among a plurality of strands, a second circuit to determine an RPO limit based on a delta value and the RPO of the eldest undispatched instruction, an ordering buffer to store entries for instructions that are waiting to be retired, and a third circuit to execute an orderable instruction from a strand from the plurality of strands to cause an entry for the orderable instruction to be inserted into the ordering buffer in response to a determination that an RPO of the orderable instruction is less than or equal to the RPO limit.