Spring-mass models have been very successful both in describing and generating running behaviors. Control of system energy within these models takes different forms, among which the use of a linear actuator in series with the leg spring has been preferred by many recent monopedal and bipedal platform designs due to its relative robustness and simplicity. However, the validity of the well-known Spring-Loaded Inverted Pendulum (SLIP) model of running for such platforms can only preserved under a specific family of control strategies to drive the actuator. In this paper, we propose a novel controller in this family, based on the idea of embedding a lossy SLIP template with a tunable damping coefficient into the linearly actuated compliant leg system. We show that this maximizes energy input within a single stride, allows decreased power requirements on the actuator compared to alternative methods, while preserving the validity and accuracy of analytic solutions and model-based controllers. We present systematic simulations to establish performance gains with respect to the commonly investigated method of modulating leg stiffness. Enabling the most efficient use of actuator power in this manner while preserving analytic tractability will allow efficient and accurate control of running for linearly actuated compliant leg designs.