Maritime transportation is the prevalent mode of transport for overseas freight, and it is frequently recognised as a relatively environmentally sustainable means of transport. However, shipping is still a substantial source of greenhouse gas emissions. We investigate the effect on fuel consumption and emissions when container ships are sailing below the design speed (i.e., slow steaming) as a strategy to minimise fuel consumption and costs. The estimation of ship fuel oil consumption is commonly based on the cubic speed¿power relation as a bottom-up approach. Nevertheless, the cubic relation could overestimate the impact of slow steaming on fuel consumption reduction and the emissions assessment. We compare real fuel consumption data and the consequent emissions with the results of assessing these parameters with the mentioned bottom-up approach. The analysis uses a set of container-ship slow steaming voyages, and the assessment is supported by speeds obtained from the Automatic Identification System (AIS). The exponential values obtained for the speed¿power relation range between 3.1 and 3.5, finding an overrating over 20% in all the cases analysed. Finally, we use a weather ship routing optimisation software to investigate additional emissions savings in the framework of ship-specific measures when weather ship routing and slow steaming are applied simultaneously.