This paper presents a new speech enhancement algorithm based upon an undecimated discrete wavelet transform followed by spectral peak enhancement. Experimental data is presented which demonstrates improved automatic speech recognition scores in noisy speech. The new algorithm first removes noise by soft-thresholding in the undecimated wavelet domain. However, the noise reduction process leaves residual noise that impairs intelligibility. In the new algorithm, residual noise removal after the undecimated wavelet denoising scheme is achieved by a nonlinear modification of the Fourier spectrum to enhance the spectral peaks relative to the valleys. Using 30 sentences at each SNR, evaluation of the new algorithm was conducted with the Connected Speech Test (CST), a procedure that ensures that the speech sentences have equal difficulty. For additive white Gaussian noise, significant improvements are observed in the experiment results and it is shown that an effective speech enhancement is obtained by spectral peak enhancement with small decomposition level. The results were variable with babble noise and office noise. Performance results will be presented