Previous research in the single machine total weighted tardiness problem (SMTWTP) has led to the proposition of effective local search strategies. At least existing benchmark instances from the literature do not pose a challenge for state-of-the-art algorithms. --- This paper describes the proposition of two classes of novel instances for the single machine total weighted tardiness problem. In response to preceding research, they are larger, thus harder to search by local search algorithms. Besides, they are computed w.r.t. control parameters that lead to comparable difficult data sets. --- In addition to providing novel instances, we report best known results, which have been computed by a Variable Neighborhood Descent algorithm.