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In this letter the focus is on linear filtering of speech before degradation due to additive background noise. The goal is to design the filter such that the speech intelligibility index (SII) is maximized when the speech is played back in a known noisy environment. Moreover, a power constraint is taken into account to prevent uncomfortable playback levels and deal with loudspeaker constraints. Previous methods use linear approximations of the SII in order to find a closed-form solution. However, as we show, these linear approximations introduce errors in low SNR regions and are therefore suboptimal. In this work we propose a nonlinear approximation of the SII which is accurate for all SNRs. Experiments show large intelligibility improvements with the proposed method over the unprocessed noisy speech and better performance than one state-of-the art method.