Overrun without payback has been proposed asa mechanism for a stack resource policy (SRP) based synchronizationprotocol for hierarchical scheduling frameworks(HSFs). In this paper we reconsider the global schedulabilityanalysis of an HSF based on two-level fixed-priority preemptivescheduling (FPPS) using overrun without payback asa mechanism. Improved analysis is presented based on theobservation that there is no need to guarantee the overrunbudget before the end of the budget period, because thatadditional amount of resources is only meant to prevent depletionof a budget during global resource access. The resultingimprovement is illustrated by means of an example. Thepossibility to discard the remainder of an overrun budget upona replenishment is briefly considered as a further improvementand its potential is shown using the same example.