Embodiment has led to a revolution in robotics by not thinking of the robot body and its controller as two separate units, but taking into account the interaction of the body with its environment. By investigating the effect of the body on the overall control computation, it has been suggested that the body is effectively performing computations, leading to the term morphological computation. Recent work has linked this to the field of reservoir computing, allowing one to endow morphologies with a theory of universal computation. In this work, we study a family of highly dynamic body structures, called tensegrity structures, controlled by one of the simplest kinds of “brains.” These structures can be used to model biomechanical systems at different scales. By analyzing this extreme instantiation of compliant structures, we demonstrate the existence of a spectrum of choices of how to implement control in the body-brain composite. We show that tensegrity structures can maintain complex gaits with linear feedback control and that external feedback can intrinsically be integrated in the control loop. The various linear learning rules we consider differ in biological plausibility, and no specific assumptions are made on how to implement the feedback in a physical system.