Advanced diffusion imaging of the spinal cord is hampered by low signal-to-noise ratio, leading to strong Rician bias in magnitude images. Here, we investigate how to mitigate such bias studying complex-valued 3T diffusion scans of the cervical cord. We test two approaches, based on decorrelated phase (DP) and total variation (TV) filtering, corroborating results with simulations. The DP and TV methods, proposed for the brain, can be applied successfully also in the cord. Moreover, they appear useful pre-processing tools for image denoising, as state-of-the-art noise removal based on Marčenko-Pastur principal component analysis (MP-PCA) performs better on complex-valued as opposed to magnitude data.