Quantitative tectonic geomorphology hinges on the analysis of longitudinal river profiles. The model behind almost all approaches in this field originates from an empirical relationship between channel slope and catchment size, often substantiated in the form of the stream-power model for fluvial incision. Significant methodological progress was recently achieved by introducing the transform. It defines a nonlinear length coordinate in such a way that the inherent curvature of river profiles due to the increase of catchment sizes in the downstream direction is removed from the analysis. However, the limitation to large catchment sizes inherited from the stream-power approach for fluvial incision persists. As a consequence, only a small fraction of all nodes of a digital elevation model (DEM) can be used for the analysis. In this study we present and discuss some empirically derived extensions of the stream power law towards small catchment sizes in order to overcome this limitation. Beyond this, we introduce a simple method for estimating the adjustable parameters in the original method as well as in our extended approaches. As a main result, an approach originally suggested for debris flow channels seems to be the best approximation if both large and small catchment sizes are included in the same analysis.