In this paper, three specific uniaxial phenomenological models commonly used for the description of a Shape Memory Alloy (SMA) behavior are examined in detail. In particular, the models examined are the Graesser-Cozzarelli model, the Wilde-Gardoni-Fujino model, and the Zhang-Zhu model. The pertinent model parameters are examined with respect to their physical representation, if any. Based on this analysis, a new simple rate-independent model is proposed which addresses all issues in a unified manner. Finally, powerful metaheuristics are employed for system identification, producing excellent fit with experimental data while revealing valuable information regarding the relative sensitivity of the proposed model parameters.