In many scheduling environments, some jobs have higher priority than others. Such scenarios are theoretically modelled by associating jobs with weights, or by having precedence constraints that limit jobs' processing order. In this paper we define and consider a new model, motivated by real-life behaviour, in which the priority among jobs is defined by a dominance hierarchy. Specifically, the jobs are arranged in hierarchy levels, and high ranking jobs are ready to accept only outcomes in which the service they receive is better than the service of subordinate jobs. We first define the model and the set of feasible schedules formally. We then consider two classical problems: minimizing the maximal tardiness and minimizing the number of tardy jobs. We provide optimal algorithms or hardness proofs for these problems, distinguishing between a global objective function and a multi-criteria objective.