Significance: Speckle noise limits the diagnostic capabilities of optical coherence tomography (OCT) images, causing both a reduction in contrast and a less accurate assessment of the microstructural morphology of the tissue.Aim: We present a speckle-noise reduction method for OCT volumes that exploits the advantages of adaptive-noise wavelet thresholding with a wavelet compounding method applied to several frames acquired from consecutive positions. The method takes advantage of the wavelet representation of the speckle statistics, calculated properly from a homogeneous sample or a region of the noisy volume. Approach: The proposed method was first compared quantitatively with different state-of-the-art approaches by being applied to three different clinical dermatological OCT volumes with three different OCT settings. The method was also applied to a public retinal spectral-domain OCT dataset to demonstrate its applicability to different imaging modalities. Results: The results based on four different metrics demonstrate that the proposed method achieved the best performance among the tested techniques in suppressing noise and preserving structural information. Conclusions: The proposed OCT denoising technique has the potential to adapt to different image OCT settings and noise environments and to improve image quality prior to clinical diagnosis based on visual assessment.