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The aim of this paper is to investigate the effect of the magnetic bunch length compression on the development of the microbunching instability. It will be shown that, after removing the linear energy chirp required for the compression, an additional and properly tuned R_{56} transport matrix element is able to dilute the initial energy modulation and to suppress the current spikes created by the microbunching instability without affecting the bunch length. A by-product of the study is the observation that a single compressor is more effective than the two-compressors scheme in reducing the unwanted modulations caused by the microbunching instability. The study is based on analytical calculations and on the simulation code elegant.