We critically re-examine the concept of a throat in a porous medium as a geometric quantity defined independently of an entry meniscus in a drainage process. To maintain the standard notion of a throat as a locally minimum-area cross section in the pore network, we demonstrate with examples that throats must intersect each other. Using flow simulation, we show that these intersecting throats correspond to capillary pressure controlled entry points during drainage. We have designed a throat-finding algorithm that explicitly locates intersecting throats, using a planar approximation for robustness and speed. The capability of the new algorithm was compared against an existing algorithm in the construction of pore-throat networks from X-ray computed tomography images of consolidated sandstones (7.5–22% porosity) and of an unconsolidated sand pack (32.5% porosity). We show that the probability of throat intersection increases significantly with porosity above 20%; in the sand pack, over 1/4 of all throats intersect with another.