This paper describes a new method of choosing between a simple linear and a two-phase linear reduced major axis regression model. For continuous two-phase linear models, differential evolution is used to estimate the parameters. The method can be used with either ordinary least squares or reduced major axis regression. There are no other methods in the literature for fitting two-phase reduced major axis regressions. Our new method is applied to problems in zebrafish kinetics bedload transport and a classic linear model of cricket chirping. Copyright © 2013 John Wiley & Sons, Ltd.