Noise masking threshold (NMT) has been extensively applied in wavelet-based speech enhancement. A gain factor is typically derived according to the NMT to suppress the additive noise. This investigation proposes a gain factor in each wavelet subband subject to a perceptual constraint. This perceptual constraint preserves the wavelet coefficients (WCs) of noisy speech when the level of residual noise is smaller than the NMT. If the residual noise level exceeds the NMT, then the wavelet coefficients of noisy speech are suppressed to reduce the corrupting noise. A lower bound on the gain factor is also proposed to prevent low-SNR regions, such as unvoiced signal, from being over-attenuated. Experimental results show that the proposed approach improves the naturalness, and does not cause annoying residual noise in the enhanced speech.