Water and debris flows exiting confined valleys have a tendency to deposit sediment on steep fans. On alluvial fans where water transport of gravel predominates, channel slopes tend to decrease downfan from ???0.10-0.04 to ???0.01 across wide ranges of climate and tectonism. Some have argued that this pattern reflects grain-size fining downfan such that higher threshold slopes are required just to entrain coarser particles in the waters of the upper fan, whereas lower slopes are required to entrain finer grains downfan (threshold hypothesis). An older hypothesis is that slope is adjusted to transport the supplied sediment load, which decreases downfan as deposition occurs (transport hypothesis). We have begun to test these hypotheses for alluvial fan long-profiles using detailed hydraulic and particle-size data in sediment transport models. On four alluvial fans in the western U.S., we find that channel hydraulic radiiare largely 0.5-0.9 m at fan heads, decreasing to 0.1-0.2 m at distal margins. We find that median gravel diameter does not change systematically along the upper 60%-80% of active fan channels as slope declines, so downstream gravel fining cannot explain most of the observed channel slope reduction. However, as slope declines, channel-bed sand cover increases systematically downfan from areal fractions of <20% above fan heads to distal fan values in excess of 70%. As a result, entrainment thresholds for bed material might decrease systematically downfan, leading to lower slopes. However, current models of this effect alone tend to underpredict downfan slope changes. This is likely due to off-channel gravel deposition. Calculations that match observed fan long-profiles require an exponential decline in gravel transport rate, so that on some fans approximately half of the load must be deposited off channel every -0.20-1.4 km downfan. This leads us to hypothesize that some alluvial fan long-proffies are statements about the rate of overbank deposition of coarse particles downfan, a process for which there is currently no mechanistic theory. ?? 2007 Geological Society of America.