•We investigate nonwetting phase (air and oil) invasion in brine-saturated sandstone.•Snap-off during drainage is observed in all experiments and in simulation results.•Current models of drainage which assume connected phase invasion are incomplete. We study quasi-static drainage displacement experiments in Bentheimer sandstone micro-cores using X-ray computed microtomography. Two nonwetting fluids, air and n-decane, are investigated, under high and low flow rate conditions. Experimental conditions consider viscosity ratios that vary by a factor of 40, and capillary numbers that range five orders of magnitude; but all experiments investigated are conducted under nominally capillary-dominated conditions, indicating that drainage displacements should demonstrate percolation-like invasion patterns. However, we observe significant and prevalent snap-off of nonwetting phase under all experimental conditions, a phenomena not predicted by the conceptual model of percolation invasion. We further observe that the size and persistence of snapped-off ganglia are influenced by the experimental flow rate and the nonwetting phase fluid. The quasi-static experimental observations are supported by lattice-Boltzmann modelling of drainage dynamics. These findings indicate that current conceptual models of drainage are incomplete, with implications for future experimental and modelling studies as well as engineering applications.