In practice, semi-active suspensions provide better tradeoffs between performances and costs than passive or active damping. Many different semi-active control algorithms have been developed, including skyhook (SH), acceleration-driven-damper (ADD), power-driven-damper (PDD), mixed SH and ADD (SH-ADD), and others. Among them, it has been shown that the SH-ADD is quasi-optimal in reducing the sprung mass vibration. In this paper, we analyze the abilities of vehicular suspension components, the shock absorber and the spring, from the perspective of energy transfer between the sprung mass and the unsprung mass, and propose a new sprung mass control algorithm named mixed SH and PDD (SH-PDD). The proposed algorithm defines a switching law that is capable of mixing SH and PDD, and simultaneously carries their advantages to achieve a better suspension performance. As a result, the proposed SH-PDD is effective in reducing the sprung mass vibration across the whole frequency spectrum, similar to SH-ADD and much better than SH, PDD, and ADD, while eliminating the control chattering and high-jerk behaviors as occurred in SH-ADD. The superior characteristics of the SH-PDD are verified in numerical analysis as well as experiments. In addition, the proposed switching law is extended to mix other semi-active control algorithms such as the mixed hard damping and soft damping, and the mixed SH and clipped-optimal linear quadratic regulator (LQR).