This paper addresses stiffness modulation and antagonistic actuation in lightweight tendon-driven bio-inspired manipulators suitable for safe interactions. Designing manipulators with variable stiffness is of great interest in human-robot collaboration tasks. Remote actuation with tendons allows inertia reduction and, if the tendons are properly routed, makes it possible to tune joint stiffness. The way in which the tendons are connected to the bodies for their actuation requires attention. Pulleys are often used to ensure a constant lever arm. However this approach does not allow antagonistic forces to change the joint stiffness. The condition for allowing an increase in stiffness via an increase in antagonistic forces is established. Then this condition is used to propose a new bio-inspired variable-stiffness joint.