We propose a new “Water-Only Look-Locker Inversion recovery” (WOLLI) sequence, based on MOLLI, that enables water-selective T1-mapping in an 8hb breath-hold at 3T. WOLLI uses a hypergeometric (HG) inversion pulse to selectively invert water with negligible effect on fat. To separate the steady-state fat and water signals, WOLLI adds one or more fat-inversions starting from the plateau of the water T1* recovery. WOLLI uses an extended Deichmann-Haase formula to correct for readout-induced saturation. We validated this approach by simulations, scans in a phantom containing 19 fat/water mixtures, and liver scans in 12 subjects (volunteers and liver disease patients).