This paper investigates the pattern of international transport costs over time, using information contained in the US imports flows over 1974-2013. First, we document the importance of the per-unit (additive) component of transport costs. We thus find that additive costs are quantitatively sizable, representing between one third and one half of overall transport costs. Second, we identify the respective roles of the reduction in "pure'' transport costs and trade composition effects in the downward trend of international transport costs, in the same spirit as Hummels (2007). Unlike him, we find that trade composition effects do not matter much and, when they do, they tend to amplify (rather than reduce) the decrease in pure transport costs. Importantly, this difference of results can be attributed to the new way of modeling the per-unit component of transport costs we offer. In both aspects, our results point to the importance of the additive component in accounting for international transport costs.