Landscape evolution models that define bedrock channel incision as driven by unit stream power or shear stress generally assume that channel width (w) and drainage area (A) in mountain channels scales as the classic hydraulic geometry of alluvial channels where w = cA^b. Previous work in mountain channel networks from coastal Oregon and Washington support the assumption used in many landscape evolution models that an alluvial hydraulic geometry relationship where b = 0.3 to 0.5 holds for bedrock channel systems (Montgomery and Gran, 2001). However, Lave and Avouac (2001) reported downstream decrease in channel width through areas of rapid uplift that were well documented by elevated terraces. Here we report field surveys from the Yarlung Tsangpo and Po-Tsangpo Rivers in eastern Tibet that indicate a systematic departure from classical width versus drainage area relations for channels flowing through drainage basins with strong longitudinal gradients in long-term rock uplift rates. These rivers flow through the eastern syntaxis of the Himalaya where young deeply exhumed metamorphic rocks in the downstream portions of the basin contrast with relatively flat lying Mesozoic sedimentary rocks in basin headwaters. Initially, channel width generally increases downstream, but then does not increase further despite large increases in drainage area as the river steepens through more deeply exhumed, and presumably more rapidly eroding, reaches. Finally, channel width systematically decreases downstream for some distance through the Namche Barwa gorge, an area predicted to have the highest bedrock incision rates in the Himalaya (Finlayson et al., 2002). The adjustment of bedrock channel width to spatial gradients in rates of rock uplift demonstrates the potential for a feedback in which greater rock uplift rates lead to channel constriction with leads to faster erosion, and therefore faster rock uplift.