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This paper describes a novel two-stage search technique which is intended to support the configuration of time-triggered schedulers for use with resource-constrained embedded systems which employ a single processor. Our overall goal is to identify a scheduler implementation which will ensure that: 1) all task constraints are met; 2) CPU power consumption is "as low as possible"; and 3) a fully cooperative scheduler architecture is employed whenever possible. Our search process is not exhaustive, and it might be described as "best characteristics first" approach. We proceed iteratively, stopping the search when we have identified the first workable solution. We assume that - because we have begun the search with "best characteristics" - any schedule identified will represent a good (but not necessarily completely optimal) solution. We show that the proposed configuration algorithm is highly effective. We also demonstrate that the algorithm has much lower complexity than alternative "branch and bound" search schemes. We conclude by making some suggestions for future work in this area.