This paper presents a speech enhancement method, where an adaptive threshold is statistically determined based on Gaussian modeling of Teager energy (TE) operated perceptual wavelet packet (PWP) coefficients of noisy speech. In order to obtain an enhanced speech, the threshold thus derived is applied upon the PWP coefficients by employing a Gaussian pdf dependent custom thresholding function, which is designed based on a combination of modified hard and semisoft thresholding functions. 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 is found to outperform some of the state-of-the-art speech enhancement methods not only at at high but also at low levels of SNRs in the sense of standard objective measures and subjective evaluations including formal listening tests.