Despite limited accuracy, MOLLI remains popular for T1 mapping due to high precision and visual quality of the maps. This is due primarily to the large dynamic range afforded by the inversion-recovery (IR) acquisition. Methods using saturation-recovery (SR) have better T1 accuracy but have relatively poor precision compared with MOLLI. This work presents a true hybrid IR/SR acquisition that targets the optimal regions of both the IR and SR relaxation curves, employs a novel method for maximizing dynamic range, and uses an improved sampling strategy. The proposed hybrid method combines the accuracy of single-point SR with the precision of IR.