This paper describes an optimal ripple-free deadbeat controller for SISO linear sampled-data plant models. A step reference is assumed and the deadbeat horizon is considered to be one of the designer's choices. The cost function to be minimized is a cumulative index that penalizes the time-weighted squared tracking error (i.e., it corresponds to an ITSE cost term). The corresponding optimization problem turns out to be convex, leading to closed form solutions. Examples are included to illustrate the main results.