A remote replication solution for a storage system receives a stream of data including independent streams of dependent writes. The method is able to discern dependent from independent writes. The method discerns dependent from independent writes by assigning a sequence number to each write, the sequence number indicating a time interval in which the write began. It then assigns a horizon number to each write request, the horizon number indicating a time interval in which the first write that started at a particular sequence number ends. A write is caused to be stored on a storage device, and its horizon number is assigned as a replication number. Further writes are caused to be stored on the storage device if the sequence number associated with the writes is less than the replication number.