Long-tailed crustaceans swim by rhythmically moving limbs called swimmerets.Over the entire biological range of animal size and paddling frequency,movements of adjacent swimmerets maintain an approximate quarter-period phase-difference with posterior limbs leading the cycle.We show that this frequency-invariant stroke-pattern is the most mechanically efficient paddling rhythm across a wide range of Reynolds numbers and that the organization of the neural circuit underlying limb coordination provides a robust mechanism for generating this stroke-pattern.