Trail-Braking (TB) is a common cornering technique used in rally racing to negotiate tight corners at (moderately) high speeds. In a previous paper by the authors it has been shown that TB can be generated as the solution to the minimum-time cornering problem, subject to fixed final positioning of the vehicle after the corner. A TB maneuver can then be computed by solving a non-linear programming (NLP). In this work we formulate an optimization problem by relaxing the final positioning of the vehicle with respect to the width of the road in order to study the optimality of late-apex trajectories typically followed by rally drivers. We test the results on a variety of corners. The optimal control inputs are approximated by simple piecewise linear input profiles defined by a small number of parameters. It is shown that the proposed input parameterization can generate close to optimal TB along the various corner geometries.