Most existing wavelet denoising techniques are developed for additive white Gaussian noise. In their applications to speckle reduction in SAR imagery, the traditional approach is to first perform a logarithmic transformation to convert the multiplicative noise model to an additive model, and then after wavelet denoising is performed on the log-transformed image, an exponential operation has to be implemented for radiometric preservation. In this paper, we introduce a low-complexity wavelet-based SAR speckle reduction algorithm which omits both the log-transform and the exponential transform operations. We decompose the multiplicative speckle model into an additive model with signal-dependent noise. Then, in the wavelet domain, we derive the shrinkage factor for each wavelet coefficient by applying the Minimum Mean Square Error (MMSE) estimation procedure. Simulated SAR images are used to evaluate the denoising performance of our proposed algorithm along with another wavelet-based denoising algorithm that involves the log-transform and exponential operation, as well as the refined Lee speckle filter. Experimental results show that the proposed filter outperforms the other filters in most cases.