An interesting feature of Sliced Inverse Rregression (SIR) is that it allows the construction of indices, as linear combinations of the multidimensional explanatory variable, most associated (in some sense) with the response variable under study. This type of method is very useful in non-linear regression contexts. The problem of variable selection in this context is important. In this paper we present two approaches based on soft thresholding or hard thresholding of the SIR interest matrix. We show how to select the hyper-parameter of the thresholding considered and we present the numerical performances of these new methodologies obtained in simulations.