A denoising method for Diffusion Tensor Imaging is proposed, with the aim to reduce the presently used clinical voxelsize of 8 ~ 27 mm3 to approximately 1 mm3. The method combines voxelwise averaging, nonlinear filtering and Rician bias correction of the directly measured Diffusion Weighted Images. To eliminate residual noise, a final postfiltering procedure applied to DTI quantities is performed. The method is based on the Delta Method formalizing the asymptotic Gaussian limit of nonlinear noise propagation. The method is explored via Monte Carlo simulations on human brain data measured with 1x1x1 mm3 resolution. The numerical results indicate the feasibility of quantitative analysis of Diffusion Tensor data of the human brain with 1 mm3 resolution, measured with clinical scanning parameters, under the assumption that thermal noise effects are the dominating artifacts.