Imaging findings inconsistent with those expected at specific chronological age ranges may serve as early indicators of neurological disorders and increased mortality risk. Estimation of chronological age, and deviations from expected results, from structural MRI data has become an important task for developing biomarkers that are sensitive to such deviations. Complementary to structural analysis, diffusion tensor imaging (DTI) has proven effective in identifying age-related microstructural changes within the brain white matter, thereby presenting itself as a promising additional modality for brain age prediction. Although early studies have sought to harness DTI's advantages for age estimation, there is no evidence that the success of this prediction is owed to the unique microstructural and diffusivity features that DTI provides, rather than the macrostructural features that are also available in DTI data. Therefore, we seek to develop white-matter-specific age estimation to capture deviations from normal white matter aging. Specifically, we deliberately disregard the macrostructural information when predicting age from DTI scalar images, using two distinct methods. The first method relies on extracting only microstructural features from regions of interest. The second applies 3D residual neural networks (ResNets) to learn features directly from the images, which are non-linearly registered and warped to a template to minimize macrostructural variations. When tested on unseen data, the first method yields mean absolute error (MAE) of 6.11 years for cognitively normal participants and MAE of 6.62 years for cognitively impaired participants, while the second method achieves MAE of 4.69 years for cognitively normal participants and MAE of 4.96 years for cognitively impaired participants. We find that the ResNet model captures subtler, non-macrostructural features for brain age prediction.