Three-dimensional (3D) deconvolution microscopy is very effective in improving the quality of fluorescence microscopy images. In this work, we present an efficient approach for the deconvolution of 3D fluorescence microscopy images based on the recently developed PURE-LET algorithm. By combining multiple Wiener filtering and wavelet denoising, we parametrize the deconvolution process as a linear combination of elementary functions. Then the Poisson unbiased risk estimate (PURE) is used to obtain the optimal coefficients. The proposed approach is non-iterative and outperforms existing techniques (usually, variants of Richardson-Lucy algorithm) both in terms of computational efficiency and quality. We illustrate its effectiveness on both synthetic and real data.