Single-shot methods suitable for determining capillary pressure and relative permeability curves in petroleum reservoir core plugs are proposed. Three classes of measurement are outlined. (i) Measurements undertaken with steady state gas flow and stationary water or oil phases in the rock. SPRITE (Single-Point Ramped Imaging with T1 Enhancement) MRI (Magnetic Resonance Imaging) spin density images map spatially varying fluid content. (ii) Similar measurements are proposed with a stationary gas phase and flowing water or oil phases. (iii) Measurements are also possible with either water or oil as the stationary phase, with the other phase undergoing steady state flow. In all cases the outflow boundary condition is maintained, capillary pressure zero, by washing the outlet face of the sample with the stationary fluid phase.