Variable selection is of major interest for highly multivariate sensors (like NIRS) , either as a robust modeling approach or for the design of multi-wavelength devices. It is especially challenging when : (1) a parcimonious selection is desired and (2) multiple responses are addressed. The CovSel method, presented in this contribution, tackles these two problems simultaneously (1) by selecting variables step by step on the basis of their global covariance with all the responses ; (2) by projecting the data orthogonally to the selected variable.