The dual-tree complex wavelet transform (CDWT) is a relatively recent enhancement to the discrete wavelet transform (DWT), with important additional properties. It is nearly shift-invariant and directionally selective in two and higher dimensions. In this letter, a locally adaptive denoising algorithm is applied to reduce speckle noise in time-domain optical coherence tomography (OCT) images of the prostate. The algorithm is illustrated using DWT and CDWT. Applying the CDWT provides improved results for speckle noise reduction in OCT images. The cavernous nerve and prostate gland can be separated from discontinuities due to noise, and image quality metrics improvements with a signal-to-noise ratio increase of 14 dB are attained.