Although most natural streams have concave-upward longitudinal profiles, there are conflicting perspectives about whether an alluvial channel is less concave than a bedrock channel. Alluvial channels can be classified as coarse-bed and fine-bed channels, depending on the bed grain size. Both are transport limited, but the threshold of motion differs greatly. Whereas a coarse-bed alluvial channel can be claimed to be as concave as a bedrock channel, we claim that a fine-bed channel is distinguishably less concave. We derive the concavity index of a fine-bed alluvial channel using the power-law relationships emergent at a steady-state river network. For known ranges of the scaling parameters, our formulation informs a range of concavity index as 0.07 ± 0.09 for a fine-bed alluvial channel. Our analyses of previous laboratory experiments and real fine-bed alluvial channels in the midwestern U.S. and northern Europe also support our conclusions, i.e., small profile concavity of steady-state fine-bed alluvial channels.