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When noise reduction (NR) and dynamic compression (CP) systems are concatenated in a hearing aid or in a cochlear implant we observe undesired interaction effects like the degradation of the global SNR. A reason for this might be that the optimization of the NR algorithm is performed with respect to the uncompressed clean speech only. In this contribution we propose an alternative approach which integrates the CP task in the derivation of the NR algorithm. By this we get novel MMSE and MAP optimal estimators for the compressed clean speech. An analysis of the behavior of the proposed solutions reveals that the differences to a serial concatenation of NR and CP are in general small. In case of the widely used MMSE log spectral amplitude (LSA) estimator [1] we show that the combined optimization is identical to a serial concatenation.