Totally ordered shared logs have become a key component in modern distributed systems, serving as a building block to ensure consistent execution of operations across replicas and partitions. A key challenge in designing this type of systems is to achieve low latency appends, given that total order requires coordination among participants and, in most designs, this coordination is in the critical path of the application. We present a novel design that removes coordination from the critical path, allowing appends to the log to be executed with low latency. We first discuss how this can be achieved in a single datacenter and, subsequently, we introduce a novel technique that allows the same principles to be applied in partially-replicated geo-distributed logs.This talk presents joint work performed by R. Soares (U. Lisboa), L. Rodrigues (U. Lisboa), R. van Renesse (Cornell U.) and L. Alvisi (Cornell U.).