Slope–area analysis and the integral approach have both been widely used in stream profile analysis. The former is better at identifying changes in concavity indices but produces stream power parameters with high uncertainties relative to the integral approach. The latter is much better for calculating channel steepness. Limited work has been done to couple the advantages of the two methods and to remedy such drawbacks. Here we show the merit of the log-transformed slope–area plot to determine changes in concavities and then to identify colluvial, bedrock and alluvial channels along river profiles. Via the integral approach, we obtain bedrock channel concavity and steepness with high precision. In addition, we run bivariant linear regression statistic tests for the two methods to examine and eliminate serially correlated residuals because they may bias both the estimated value and the precision of stream power parameters. We finally suggest that the coupled process, integrating the advantages of both slope–area analysis and the integral approach, can be a more robust and capable method for bedrock river profile analysis.