Aggregated soils are structured systems susceptible to non-uniform flow. The hydraulic properties depend on the aggregate fabric and the way the aggregates are assembled. We examined the hydraulic behavior of an aggregate packing. We focused on conditions when water mostly flows through the aggregates, leaving the inter-aggregate pore space air-filled. The aggregates were packed in 3 mm thick slabs forming a quasi two-dimensional bedding. The larger aggregates were wetted with water and embedded in smaller aggregates equilibrated at a lower water content. The water exchange between wet and drier aggregates was monitored by neutron radiography. The three-dimensional arrangement of the aggregates was reconstructed by neutron tomography. The water flow turned out to be controlled by the contacts between aggregates, bottle-necks that slow down the flow. The bottle-neck effect is due to the narrow flow cross section of the contacts. The water exchange was simulated by considering the contact area between aggregates as the key parameter. In order to match the observed water flow, the contact area must be reduced by one to two orders of magnitude relative to that obtained from image analysis. The narrowness of the contacts is due to air-filled voids within the contacts.