Subglacial conduit systems are thought to consist of dendritic networks that exist at lower pressure than distributed systems and have locations that are determined by theoretical hydraulic potential. On glaciers with moulins, however, meltwater is delivered to glacier beds at discrete points, violating assumptions of uniform recharge needed to calculate potential. To understand how moulins affect subglacial conduit hydrology, we used speleological techniques to map 0.4 km of subglacial conduit at the base of a moulin in Hansbreen, Svalbard, and compared our observations with theoretical predictions. The conduit began in an area predicted to lack drainage, crossed equipotential contours at oblique rather than right angles and was locally anastomotic rather than dendritic. We propose moulin locations, which are determined by the locations of supraglacial streams and crevasses, control locations of subglacial recharge. Because conduits have no direct causal relationship with gradients in effective pressure, this recharge can form conduits in areas of glacier beds that may not be predicted by hydraulic potential theory to have conduits. Recharge by moulins allows hydraulic head to increase in conduits faster and to higher values than in adjacent distributed systems, resulting in an increase rather than a decrease in glacier sliding speeds above subglacial conduits.