The fundamental basis of T1 and T2 contrast in brain MRI is not well understood; recent literature contains conflicting views on the nature of relaxation in white matter (WM). We investigated the effects of inversion pulse bandwidth on measurements of T1 and T2 in WM. Hybrid inversion-recovery/Carr-Purcell-Meiboom-Gill experiments with broad or narrow bandwidth inversion pulses were applied to bovine WM in vitro. Data were analysed with the commonly used 1D-non-negative least squares (NNLS) algorithm, a 2D-NNLS algorithm, and a four-pool model which was based upon microscopically distinguishable WM compartments (myelin non-aqueous protons, myelin water, non-myelin non-aqueous protons and intra/extracellular water) and incorporated magnetization exchange between adjacent compartments. 1D-NNLS showed that different T2 components had different T1 behaviours and yielded dissimilar results for the two inversion conditions. 2D-NNLS revealed significantly more complicated T1/T2 distributions for narrow bandwidth than for broad bandwidth inversion pulses. The four-pool model fits allow physical interpretation of the parameters, fit better than the NNLS techniques, and fits results from both inversion conditions using the same parameters. The results demonstrate that exchange cannot be neglected when analysing experimental inversion recovery data from WM, in part because it can introduce exponential components having negative amplitude coefficients that cannot be correctly modeled with nonnegative fitting techniques. While assignment of an individual T1 to one particular pool is not possible, the results suggest that under carefully controlled experimental conditions the amplitude of an apparent short T1 component might be used to quantify myelin water.