The paper (a first version of this work was presented in Aug. 2014 at ASME-DETC in Buffalo, NY) describes a novel robot gripper for garment handling. The device has been designed, developed, prototyped, and tested within the CloPeMa European Project creating a robot system for automated manipulation of clothing and other textile items. The gripper has two degrees of freedom (dof) and includes both rigid and flexible elements. A variable-stiffness actuator has been implemented to add controlled compliance in the gripper’s operation allowing the combining of various grasping and manipulation tasks. First, we analyze the specific application-determined task requirements, focusing on the need for adaptive flexibility and the role of compliant elements in the design. The chosen solution is a simple planar mechanism, equipped with one standard and one variable-stiffness actuator. The mechanical design of the gripper, including the hydraulic system used in the biphasic actuator, is outlined, and the control architecture, using sensor feedback, is described.