Physiological noise artifacts, especially those originating from cardiac pulsation and subject motion, are common in clinical Diffusion tensor-MRI acquisitions. Previous works show that signal perturbations produced by artifacts can be severe and neglecting to account for their contribution can result in erroneous diffusion tensor values. The Robust Estimation of Tensors by Outlier Rejection (RESTORE) method has been shown to be an effective strategy for improving tensor estimation on a voxel-by-voxel basis in the presence of artifactual data points in diffusion-weighted images. In this article, we address potential instabilities that may arise when using RESTORE and propose practical constraints to improve its usability. Moreover, we introduce a method, called informed RESTORE designed to remove physiological noise artifacts in datasets acquired with low redundancy (less than 30–40 diffusion-weighted image volumes)—a condition in which the original RESTORE algorithm may converge to an incorrect solution. This new method is based on the notion that physiological noise is more likely to result in signal dropouts than signal increases. Results from both Monte Carlo simulation and clinical diffusion data indicate that informed RESTORE performs very well in removing physiological noise artifacts for low redundancy diffusion-weighted image datasets. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.