Visibility of optical coherence tomography (OCT) images can be severely degraded by speckle noise. A computationally efficient despeckling approach that strongly reduces the speckle noise is reported. It is based on discrete wavelet transform (DWT), but eliminates the conventional process of threshold estimation. By decomposing an image into different levels, a set of sub-band images are generated, where speckle noise is additive. These sub-band images can be compounded to suppress the additive speckle noise, as DWT coefficients resulting from speckle noise tend to be approximately decorrelated. The final despeckled image is reconstructed by taking the inverse wavelet transform of the new compounded sub-band images. The performance of speckle reduction and edge preservation is controlled by a single parameter: the level of wavelet decomposition. The proposed technique is applied to intravascular OCT imaging of porcine carotid arterial wall and ophthalmic OCT images. Results demonstrate the effectiveness of this technique for speckle noise reduction and simultaneous edge preservation. The presented method is fast and easy to implement and to improve the quality of OCT images.