The brain microstructure, especially myelinated axons and free fluids, may provide useful insight into brain neurodegen-erative diseases such as multiple sclerosis (MS). These may be distinguished based on their transverse relaxation times which can be measured using T 2 relaxometry MRI. However, due to physical limitations on achievable resolution, each voxel contains a combination of these tissues, rendering the estimation complex. We present a novel multi-compartment T 2 (MCT2) estimation based on variable projection, applicable to any MCT2 microstructure model. We derive this estimation for a three-gamma distribution model. We validate our framework on synthetic data and illustrate its potential on healthy volunteer and MS patient data.