The Full Velocity Difference (FVD) model is a well-recognized and widely-used time continuous car following model. Although the model has very good simulation performances in most cases, it is not applicable to some specific traffic scenarios, where it can generate very large or even overshooting accelerations or decelerations that are totally unnecessary and might be far beyond the acceleration/deceleration limits of real vehicles. In this paper, we explore the reason and attempt to correct it by proposing a confined Full Velocity Difference (c-FVD) model in which we limit the accelerations or decelerations generated by the existing FVD models to a reasonable level. The performances of both models are compared from both microscopic and macroscopic perspectives. The ability of the modified model to generate strong but reasonable decelerations to avoid accidents in urgent traffic scenarios is also validated. According to the comparative analyses, both models will have same performances in most cases while the c-FVD model will outperform the existing FVD model in certain scenarios where very large or overshooting accelerations or decelerations are involved.