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The fixed preemption point (FPP) model has been studied as an alternative to fully preemptive and non-preemptive models, as restricting preemptions to specific, predictable locations within a task’s execution can simplify overhead analysis without disallowing preemptions entirely. Prior work has produced response-time analyses for global Earliest Deadline First (G-EDF) scheduling under the FPP model. However, scheduling decisions based solely on task deadlines may be too coarsegrained and may not lead to the lowest response times. In this paper, we propose global FPP EDF-like (G-FPP-EL) scheduling, which assigns a priority point in time for each non-preemptive region of a task. We adapt compliant-vector analysis (CVA) to our model and present general response-time bounds for G-FPPEL schedulers. We then demonstrate that it is possible to design G-FPP-EL schedulers acheiving response-time bounds optimal under CVA and argue that such schedulers should replace global FPP EDF.