Current adaptive cruise control (ACC) systems on commercially-available vehicles are string-unstable. This study proposes a trajectory shaper (TS)-based method, which only modifies the trajectory information (i.e., position and speed measured by sensors) of the predecessor vehicle, so that the ego vehicle driven by a string-unstable ACC system leverages the modified trajectory information to achieve string stability. Additionally, to mitigate the negative impacts of acceleration/deceleration limit in the ACC system (which is not factored in TS), the technique of linear acceleration/deceleration relaxation (LA/D-R) is devised to augment the TS-based method. The results from numerical experiments suggest that the TS-based method and the LA/D-R technique are cost-effective during implementation, as they avoid modifying existing ACC control algorithms (which entails complex analysis of ACC control systems and parameter tuning).