Overrun without payback has been proposed as a mechanism for a stack resource policy (SRP) based synchronization protocol for hierarchical scheduling frameworks (HSFs). In this paper we reconsider the global schedulability analysis of an HSF based on two-level fixed-priority preemptive scheduling (FPPS) using overrun without payback as a mechanism. Improved analysis is presented based on the observation that there is no need to guarantee the overrun budget before the end of the budget period, because that additional amount of resources is only meant to prevent depletion of a budget during global resource access. The resulting improvement is illustrated by means of an example. The possibility to discard the remainder of an overrun budget upo...