In-vivo quantitative MRI (qMRI) aims at characterizing the biological properties of brain tissue. However, qMRI parameters are sensitive both to the molecular tissue properties and to the water content within each voxel. We introduce a novel approach that disentangles these two contributions to qMRI parameters and provides tissue-specific measurements. This is achieved by evaluating the dependency of qMRI parameters on the non-water fraction. Using phantoms, we show that this dependency changes as a function of molecular composition. In the human brain, our method reveals unique tissue signatures for different brain regions, along with region-specific age-related changes.