An end-effector of a programmable motion device, said end-effector comprising a body that provides an open interior, said open interior being coupled to a vacuum source, and said body including a contact surface for contacting an object to be grasped by the end effector, said contact surface at least partially defining an aperture, and said body including a curved flexible portion with an outer surface that faces away from the open interior, and the curved flexible portion provides that when the flow of air drawn by the vacuum source through the aperture is reduced due to the aperture being at least partially blocked, the outer surface of the curved flexible portion faces the object being grasped at least partially within the open interior of the body.