Traditionally, most of the nonlinear control techniques for elastic robotic systems focused on achieving a desired closed-loop behavior by modifying heavily the intrinsic properties of the plant. This is also the case of elastic tendon-driven systems, where the highly nonlinear couplings lead to several control challenges. Following the current philosophy of exploiting the mechanical compliance rather than fighting it, this letter proposes an Elastic Structure Preserving impedance (ESPi) control for systems with coupled elastic tendinous transmissions. Our strategy achieves a globally asymptotically stable closed-loop system that minimally shapes the intrinsic inertial and elastic structure. It further allows to impose a desired link-side impedance behavior. Simulations performed on the tendon-driven index finger of the DLR robot David show satisfactory results of link-side interaction behavior and set-point regulation.