We propose a novel design for a lightweight and compact tunable stiffness actuator capable of stiffness changes up to 20x. The design is based on the concept of a coiled spring, where changes in the number of layers in the spring change the bulk stiffness in a near linear fashion. We present an elastica nested rings model for the deformation of the proposed actuator and empirically verify that the designed stiffness-changing spring abides by this model. Using the resulting model, we design a physical prototype of the tunable-stiffness coiled-spring actuator and discuss the effect of design choices on the resulting achievable stiffness range and resolution. In the future, this actuator design could be useful in a wide variety of soft robotics applications, where fast, controllable, and local stiffness change is required over a large range of stiffnesses.