The Logical Execution Time (LET) model has deterministic timing and data-flow properties, which simplify the computation of end-to-end latencies of multi-rate cause-effect chains. However, the LET model results in pessimistic end-to-end latencies since it abstracts the underlying platform and scheduling choices. In this paper, we propose a method to reduce end-to-end latencies of multi-rate cause-effect chains applying the LET model, by considering knowledge of the schedule in later design phases of safety critical embedded systems. Our method shortens and shifts the communication intervals of the LET model. If needed, e.g., for legacy reasons, our method can be applied to a subset of tasks only. We evaluate our work based on automotive benchmarks and synthetic task sets. We compare our results with previous work and the LET model. The experiments show significant reductions of maximum reaction time and data age values.