In the context of uniprocessor scheduling, two scheduling algorithms have been very much studied: one in the class of fixed task priority (FTP) where Rate Monotonic (RM) is optimal and one in the class of fixed job priority (FJP), where Earliest Deadline First (EDF) is optimal. RM has the disadvantage of imposing processor utilization less than 100% (i.e., 69% in the worst case) while EDF scheduling can reach 100% of processor utilization. Some research have been done to overcome this sub-optimality problem. It has been shown that when periods are harmonic, the processor utilization bound of RM is identical to the one of EDF [1]. When no constraint is imposed on the periods, the dual priority approach was introduced in 1993 [3]. The scheduler consider two priorities and two phases for each task, each phase has a fixed priority, the transition from a phase to another is made at a fixed time offset from the task release. Dual priority approach is interesting as it is conjectured that a dual priority scheduling can reach the same performances as an EDF scheduler. In this paper, we revisit dual priority scheduling for uniprocessor systems with implicit-deadline periodic task set. We recall existing conjectures. Then, we explicit a new class of scheduling FPk , a fixed priority scheduling that requires at most k promotions at k fixed times. We show that dual priority and EDF scheduling are particular cases of FPk . Finally, we analyse EDF scheduling trying to study how far it is from a dual priority scheduler in terms of promotions.