The volume fraction of water related to myelin (f my) is a promising MRI index for in vivo assessment of brain myelination, that can be derived from multi-component analysis of T1 and T2 relaxometry signals. However, existing quantification methods require rather long acquisition and/or post-processing times, making implementation difficult both in research studies on healthy unsedated children and in clinical examinations. The goal of this work was to propose a novel strategy for f my quantification within acceptable acquisition and post-processing times. Our approach is based on a 3-compartment model (myelin-related water, intra/extra-cellular water and unrestricted water), and uses calibrated values of inherent relaxation times (T1 c and T2 c) for each compartment c. Calibration was first performed on adult relaxometry datasets (N = 3) acquired with large numbers of inversion times (TI) and echo times (TE), using an original combination of a region contraction approach and a non-negative least-square (NNLS) algorithm. This strategy was compared with voxel-wise fitting, and showed robust estimation of T1 c and T2 c. The accuracy of f my calculations depending on multiple factors was investigated using simulated data. In the testing stage, our strategy enabled fast f my mapping, based on relaxometry datasets acquired with reduced TI and TE numbers (acquisition <6 min), and analyzed with NNLS algorithm (post-processing <5min). In adults (N = 13, mean age 22.4±1.6 years), f my maps showed variability across white matter regions, in agreement with previous studies. In healthy infants (N = 18, aged 3 to 34 weeks), asynchronous changes in f my values were demonstrated across bundles, confirming the well-known progression of myelination.