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In time-triggered systems, where the schedule table is predefined and statically configured at design time, sporadic event-triggered (ET) tasks are handled within specially dedicated slots or when time-triggered (TT) tasks finish their execution early. We introduce a new paradigm for synthesizing TT schedules that guarantee the correct temporal behavior of TT tasks and the schedulability of sporadic ET tasks with arbitrary deadlines. The approach first expresses a constraint for the TT task schedule in the form of a maximal affine envelope that guarantees that as long as the schedule generation respects this envelope, all sporadic ET tasks meet their deadline. The second step consists of modeling this envelope as a burst limiting constraint and building the TT schedule via simulating a modified Least-Laxity-First (LLF) scheduler. Using this novel technique, we show that we achieve equal or better schedulability and a faster schedule generation for most use-cases compared to simple polling approaches. Moreover, we present an extension to our method that finds the most favourable schedule for TT tasks with respect to ET schedulability, thus increasing the probability of the computed TT schedule remaining feasible when ET tasks are later added or changed.