A direct and non-invasive measure of tissue O2 would be a major advance. O2 is paramagnetic and can thus, in principle, be quantified with NMR/MRI. However, such measurements are challenged/masked by two competing effects: (i) magnetization transfer between 1H spins of tissue water and the solid-like macromolecular matrix (e.g., proteins, cell membranes) and (ii) blood flow, which can bring equilibrium-polarized 1H spins into the interrogated tissue volume. We describe a strategy for mitigating these confounds and quantify the direct relationship between pO2 and the MR-measured longitudinal relaxation rate constant, R1.