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Characterizing the properties and orientations of sub-voxel fiber populations, although essential to study white-matter architecture, microstructure and connectivity, remains one of the main challenges faced by the MRI microstructure community. While some progress has been made in overcoming this challenge using models, signal representations and tractography algorithms, these approaches are ultimately limited by their key assumptions or by the lack of specificity of the diffusion signal alone. In order to alleviate these limitations, we combine diffusion-relaxation MR acquisitions incorporating tensor-valued diffusion encoding, Monte-Carlo signal inversions that extract non-parametric intra-voxel distributions of diffusion tensors and relaxation rates, and density-based clustering techniques. This new approach, called "Monte-Carlo density-peak clustering" (MC-DPC), first delineates clusters in the diffusion-orientation subspace of the fiber-like diffusion-relaxation components output by Monte-Carlo signal inversions and then draws from the statistical aspect of these inversion algorithms to compute the median and interquartile range of orientation-resolved means of diffusivities and relaxation rates. Evaluating MC-DPC on tensor-valued diffusion-encoded and T2-weighted correlated datasets in silico and in vivo, we demonstrate its ability to simultaneously capture sub-voxel fiber orientations and cones of uncertainty, and measure fiber-specific diffusion-relaxation properties that are consistent with the known anatomy and existing literature. Straightforwardly translatable to other diffusion-relaxation correlation experiments probing $T_1$ and $T_2^*$, MC-DPC shows potential in tracking bundle-specific patient-control group differences and longitudinal microstructural changes, enabling new tools for microstructure-informed tractography, and mapping tract-specific myelination states.