Determining the efficiency (and the economy) of a movement is a primary goal for those interested in understanding, and possibly improving, human locomotion and/or sport’s performance. This goal is particularly difficult to achieve in swimming where different “efficiencies” could be computed based on the partitioning of mechanical power output into its useful and non useful components as well as because of the difficulties in measuring the forces a swimmer can exert in water. In this paper the “possible range” of overall (gross) and propelling efficiency values for swimming humans is estimated and discussed.