This paper deals with the problem of string stability in a chain of acceleration-controlled vehicles. It is known that string stability cannot be achieved, with any linear controller, when the vehicles' control inputs are based only on relative distances to a fixed number of predecessors. We extend the set of characteristics under which string stability is impossible by including elements like dynamic sensor parts and local inter-vehicular communication, as in cooperative adaptive cruise control. It is also known that a weaker form of string stability is achievable by adding absolute velocity measurements (e.g. "time-headway" policy). We show that a stronger property can also be achieved, provided steady-state control gain is infinite e.g. by using integral control.