Nuclear magnetic resonance spin-lattice relaxation time data, obtained with the inversion-recovery pulse sequence and subsequent Fourier transformation, are analyzed by various statistical estimation procedures. The different estimation methods often give markedly different T 1 estimates. The most reliable method is shown to be iterative nonlinear estimation. Omission of explicit experimental determination of S ∞ is feasible with this method. The effect of a misadjusted flip angle on the T 1 estimates is discussed for two different estimation methods. A general nonlinear estimation method is developed suitable for the analysis of data from temperature-, frequency-, or pH-dependent T 1 studies. This method enables the simultaneous determination of frequency factors τ 0, activation energies E a, spin-rotational coupling constants C rmeff , and chemical shift anisotropies Δσ in a single step. Phosphorus-31 data are used for this study but the conclusions are not restricted to this particular nucleus.