A variety of methods, controllers and algorithms are described for controlling a vehicle to closely follow one another safely using automatic or partially automatic control. The described control schemes are well suited for use in vehicle platooning and/or vehicle convoying applications, including truck platooning and convoying controllers. In one aspect, a power plant (such as an engine) is controlled using a control scheme arranged to attain and maintain a first target gap between the vehicles. Brakes (such as wheel brakes) are controlled in a manner configured to attain and maintain a second (shorter) target gap. Such control allows a certain degree of encroachment on the targeted gap (sometimes referred to as a gap tolerance) before the brakes are actuated. The described approaches facilitate a safe and comfortable rider experience and reduce the likelihood of the brakes being actuated unnecessarily.