Fixed-priority scheduling with deferred preemption (FPDS) has been proposed in the literature as a viable alternative to fixed-priority pre-emptive scheduling (FPPS), that obviates the need for non-trivial resource access protocols and reduces the cost of arbitrary preemptions. This paper shows that existing worst-case response time analysis of hard real-time tasks under FPDS, arbitrary phasing and relative deadlines at most equal to periods is pessimistic and/or optimistic. The same problem also arises for fixed-priority non-pre-emptive scheduling (FPNS), being a special case of FPDS. This paper provides a revised analysis, resolving the problems with the existing approaches. The analysis is based on known concepts of critical instant and ...