Tensile test data for structural steels are ubiquitous. Yet, the information monotonic loading provides with respect to the material's characteristics is limited. Notably, features of inelastic response to cyclic loading, such as the Bauschinger eect, can not be determined without testing with a load reversal protocol. This paper aims at addressing this shortcoming by formulating a constrained optimization problem that provides best-t material parameters to a tensile test, while simultaneously imposing representative cyclic properties for structural steels. Recommendations on constraints are given. Results demonstrate that improvements can be achieved when compared to: (1) direct ts to tensile data and (2) input model parameters from the same steel material but from different batches calibrated to a wide range of strain-based protocols. Given the available data, it is concluded that simpler models with one backstress tend to perform best with the proposed constraints.