In this article we describe the precision in the estimation of the spin-lattice relaxation time T1 from MRI signals acquired for various flip angles with the repetition time TR held constant. We review the estimation procedure itself and present a model for the propagation of noise in the signal into the calculated T1. This model is verified by both Monte Carlo simulations and experimental data taken on image phantoms. Based on this model, we find that for a given TR/T1 there exist two optimal flip angles that will minimize the uncertainty in the estimated T1. We also show how two optimal angles can be selected for a given range of TR/T1 values. In addition, T1 estimation using the two optimal angles can be comparable to or better than using multiple evenly spaced angles. Finally, in an initial comparison with the two-point saturation recovery method of calculating T1, results for equal total scanning time TRTot suggest that for T1 greater than 0.5 TRTot, the limited flip angle approach gives better T1 precision whereas for T1 less than 0.5 TRTot the saturation recovery approach is better.