Travel represents a major cost for many animals so there should be selection pressure for it to be efficient – at minimum cost. However, animals sometimes exceed minimum travel costs for reasons that must be correspondingly important. We use Dynamic Body Acceleration (DBA), an acceleration-based metric, as a proxy for movement-based power, in tandem with vertical velocity (rate of change in depth) in a shark (Rhincodon typus) to derive the minimum estimated power required to swim at defined vertical velocities. We show how subtraction of measured DBA from the estimated minimum power for any given vertical velocity provides a “proxy for power above minimum” metric (PPAmin), highlighting when these animals travel above minimum power. We suggest that the adoption of this metric across species has value in identifying where and when animals are subject to compelling conditions that lead them to deviate from ostensibly judicious energy expenditure