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Coarse-grained reconfigurable architectures appear as a scalable solution to embedded system design, with a reduced reconfiguration time, memory footprint, as well as placement and routing complexity. To ensure high performance, data must be efficiently delivered to the reconfigurable matrix. For that, several architectures propose the use of fully interconnected local networks, as crossbar or large multiplexers. However, these interconnections are very area consuming. Therefore, in order to reduce the interconnection complexity without losing performance, this work proposes to use Multistage Interconnection Networks. As a case study, we have implemented the proposed approach in a tightly coupled reconfigurable array, which works together with a MIPS processor. Simulation results over the Mibench Benchmark set show savings of up to 26% of the total area, with a decrease of only 1% on the average performance.