The geometry of channels controls the erosion rate of rivers and the evolution of topography following environmental change. We examine how sediment, slope, and substrate interact to constrain the development of channels following deglaciation and test whether theoretical relationships derived from streams reacting to tectonic uplift apply in these settings. Using an extensive data set of channel geometry measurements from postglacial streams in the Scottish Highlands, we find that a power law width-drainage area scaling model accounts for 81% of the spatial variation in channel width. Substrate influences channel form at the reach scale, with bedrock channels found to be narrower and deeper than alluvial channels. Bedrock channel width does not covary with slope, which may be due to downstream variations in sediment flux. Bedrock channel width-to-depth ratios increase with discharge (or area) and sediment flux, consistent with increasing bed cover promoting lateral widening. We find steep, wide, and shallow bedrock channels immediately below lakes, which we interpret as the result of limited erosion due to a lack of sediment "tools." Where sediment supply is sufficient to exceed transport capacity, alluvial channels develop wider, shallower geometries constrained primarily by flow hydraulics. Our results indicate that simple scaling models of channel width with drainage area are applicable at regional scale, but locally, channel width varies with substrate, and in the case of bedrock channels, with sediment flux..