The two perspectives of autonomous driving and new active safety in vehicles are complementary, and both hold promise to reduce the number of accidents and associated severe or fatal injuries. They both coincide in the recent interest in finding alternatives to traditional yaw-control systems that can utilize the full potential of the vehicle. By considering the control problem as that of lane-keeping, also at high speed and at-the-limit of tire friction, rather than that of yaw control, leads to the possibility of optimization-based active-braking systems with better performance than those existing today. Here, we investigate the optimal braking patterns in completely autonomous lane-keeping maneuvers resulting from a formulation where the optimization criterion used is an interpolation between the initial and final velocities of the maneuver. Varying the interpolation parameter, i.e., the relative weight between the initial and final velocity, results in different vehicle behavior. The analysis of these behaviors provides several new insights into stabilizing braking patterns for vehicles in at-the-limit maneuvers. Specifically, it is to be noted that the benefits of a lane-keeping strategy are immediate, both in terms of the maximum possible initial velocity and the velocity reduction. The formulation embeds the traditional yaw control and optimal lane-keeping as the end-point values of the interpolation parameter, and adds a continuous family of behaviors in between. This gives a new perspective for investigating the relation between traditional yaw control and optimal lane-keeping for autonomous vehicles.