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This paper is based on a conjecture that the more confidence one needs in a task execution time bound (the less tolerant one is of missed deadlines), the larger and more conservative that bound tends to become in practice. We assume different tasks perform functions having different criticalities and requiring different levels of assurance. We assume a task may have a set of alternative worst-case execution times, each assured to a different level of confidence. This paper presents ways to use this information to obtain more precise schedulability analysis and more efficient preemptive fixed priority scheduling. These methods are evaluated using workloads abstracted from production avionics systems.