Soft robots actuated by inflation of a pneumatic network (a pneu-net) of small channels in elastomeric materials are appealing for producing sophisticated motions with simple controls. Although current designs of pneu-nets achieve motion with large amplitudes, they do so relatively slowly (over seconds). This paper describes a new design for pneu-nets that reduces the amount of gas needed for inflation of the pneu-net, and thus increases its speed of actuation. A simple actuator can bend from a linear to a quasi-circular shape in 50 ms when pressurized at P = 345 kPa. At high rates of pressurization, the path along which the actuator bends depends on this rate. When inflated fully, the chambers of this new design experience only one-tenth the change in volume of that required for the previous design. This small change in volume requires comparably low levels of strain in the material at maximum amplitudes of actuation, and commensurately low rates of fatigue and failure. This actuator can operate over a million cycles without significant degradation of performance. This design for soft robotic actuators combines high rates of actuation with high reliability of the actuator, and opens new areas of application for them.