Squid are the largest jet propellers in nature as adults, but as paralarvae they are some of the smallest, faced with the inherent inefficiency of jet propulsion at a low Reynolds number. In this study we describe the behavior and kinematics of locomotion in 1 mm paralarvae of Dosidicus gigas , the smallest squid yet studied. They swim with hop-and-sink behavior and can engage in fast jets by reducing the size of the mantle aperture during the contraction phase of a jetting cycle. We go on to explore the general effects of a variable mantle and funnel aperture in a theoretical model of jet propulsion scaled from the smallest (1 mm mantle length) to the largest (3 m) squid. Aperture reduction during mantle contraction increases propulsive efficiency at all squid sizes, although 1 mm squid still suffer from low efficiency (20%) because of a limited speed of contraction. Efficiency increases to a peak of 40% for 1 cm squid, then slowly declines. Squid larger than 6 cm must either reduce contraction speed or increase aperture size to maintain stress within maximal muscle tolerance. Ecological pressure to maintain maximum velocity may lead them to increase aperture size, which reduces efficiency. This effect might be ameliorated by nonaxial flow during the refill phase of the cycle. Our model's predictions highlight areas for future empirical work, and emphasize the existence of complex behavioral options for maximizing efficiency at both very small and large sizes.