Many recent experiments have shown that the current commercially available adaptive cruise control (ACC) systems demonstrate string instability phenomena. The lower-level time-lag, the sensor time-delay, and the input disturbance primarily contribute to such instability. This paper presents a unified strategy to design ACC systems compensating the lower-level time-lag, the sensor time-delay, and the input disturbance, by fulfilling the over-damped string stability criterion for homogeneous platoons. The over-damped feature associated with string stability explicitly addresses the safety of a platoon in a stricter sense, considering the transient convergence effects, such as over-shoot, under-shoot, and oscillations, and satisfying all the Lp stability norms, where p∈1,∞. In this article, the derived over-damped string-stable strategy compensating lag, delay, and disturbance (OSSCLDD) is presented in a general unified form that applies to any linear or convex velocity-dependent spacing functions. The derived strategy is demonstrated and validated via simulation using a linear constant time gap spacing function and two nonlinear spacing functions, namely, the variable time gap and the quadratic range spacing function.