In a previous paper [Oper. Res. 31, 114-127 (1983; Zbl 0495.90046)] the authors and {\it F. Roubellat} developed a dominance property relative to the feasibility of job sequences constrained by limit times when using a single machine. These results are here transposed and interpreted for tardiness optimization purpose. An application is presented with a view to improving the performance of the branch and bound algorithm proposed by {\it K. R. Baker} and {\it Z. Su} [Nav. Res. Logist. Q. 21, 171-176 (1974; Zbl 0277.90044)] to find the sequence which minimizes maximum tardiness.