T2 relaxation decay curves from in vivo human brain tissue are rarely mono-exponential due to both physiology and partial volume averaging. We propose a tri-exponential model, parametric fitting of the T2 relaxation curve, restricting the range for the T2 in each compartment, and estimating the probability of the existence of each of the components on a voxel-by-voxel basis. The model quantifies the T2 into three discrete compartments: Myelin (T2 short = 20-50 ms), White / Gray Matter (T2 middle = 50-120 ms), and CSF (T2 long = 120-500 ms). A constrained nonlinear minimization technique using subspace trust-region methods was implemented. A voxel-by-voxel analysis was performed, and for any given voxel, the three T2 components were forced to lie within each compartment. However, the magnitude for each of these components was allowed to take any non-negative value including zero. As a result, if any component were absent, its magnitude would be zero and hence not contribute to the fit. Results from the processing of six healthy normal adults, imaged on a 3T magnet with clinically viable imaging protocols, have been presented and are shown to be in excellent agreement with reported values. This technique is robust and accurate and may potentially be useful in aiding clinical diagnosis and follow-up of patients with white matter abnormalities.