Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Further, we discretize the set of velocity profiles along a given path into a selection of longitudinal jerk way-points along the path. Finally, we repeatedly solve the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.