This paper extends previous work in Escribano and Jorda (1997) and introduces new LM specification procedures to choose between Logistic and Exponential Smooth Transition Regression (STR) Models. These procedures are simpler, consistent and more powerful than those previously available in the literature. An analysis of the properties of Taylor approximations around the transition function of STR models permits one to understand why these procedures work better and it suggests ways to improve tests of the null hypothesis of linearity versus the alternative of STR-type nonlinearity. Monte-Carlo experiments illustrate the performance of the different tests introduced. The new procedures are then implemented on a study of the dynamics of the U.S. unemployment rate.