For enhancement of noisy speech, a method of threshold determination based on modeling of Teager energy (TE) operated perceptual wavelet packet (PWP) coefficients of the noisy speech by exponential distribution is presented. A custom thresholding function based on the combination of mu-law and semisoft thresholding functions is designed and exploited to apply the statistically derived threshold upon the PWP coefficients. The effectiveness of the proposed method is evaluated for car and multi-talker babble noise corrupted speech signals through performing extensive simulations using the NOIZEUS database. The proposed method outperforms some of the state-of-the-art speech enhancement methods both at high and low levels of SNRs in terms of the standard objective measures and the subjective evaluations including formal listening tests.