One of the major advantages of soft grippers – the fact that they are soft - is also sometimes one of their limitations. While highly compliant materials allow these grippers to conform around and grasp objects, it also limits the amount of force that these actuators can support. Here, we present a compact, prehensile and soft gripper capable of varying its stiffness on demand, allowing not only grasping but also manipulation of objects. The gripper consists of fluidic chambers within a silicone structure and two electrostatic clutches bonded to opposite external surfaces. An integrated electrohydrodynamic pump is used to pressurize the fluidic chambers. This pump requires no moving parts, instead operating on the ‘ion-drag’ principle of ionizing and accelerating a dielectric liquid. As a result, these pumps are light, compact and draw only mW levels of power, allowing easy integration with the gripper to create a self-contained actuator. The gripper is actuated by pressurizing the chambers while simultaneously blocking one of the clutches, causing the structure to bend around and grasp an object. Once the object is grasped, the second clutch is blocked, increasing the bending stiffness of the structure and allowing the object to be manipulated. Furthermore, the use of this variable-stiffness configuration allows bi- directional bending using only a single pressure source. We believe our approach adds significant versatility to soft gripper applications.