Sensitivity-based model updating entails a computational parameter estimation problem, in which a set of model parameters is adjusted to minimize the discrepancy between identified system features and the corresponding model predictions. In order to promote the posedness and conditioning of the estimation problem, it is often necessary to exclude some of the uncertain parameters and accept the errors induced by treating them at their nominal values. The present paper proposes a parameter rejection scheme that seeks to mitigate the noted errors by minimizing the sensitivity of the estimation problem to changes in the excluded parameters. The sensitivity minimization is realized in a closed-loop setting with output feedback eigenstructure assignment, which, given that the operation is offline, can be implemented through processing of open-loop input-output data. Consequently, the scheme rests on the assumption that open-loop input-output data can be collected while the considered system is linear and time-invariant. The implementation and validity of the scheme are demonstrated in the context of numerical and experimental examples with vibrating systems. • A scheme is presented for parameter rejection in sensitivity-based model updating. • The sensitivity of the updating solution to the rejected parameters is minimized. • The rejection formulation uses static output feedback eigenstructure assignment. • The feedback is realized virtually by processing of available input-output data. • The eigenstructure assignment is posed as a homogeneous system of equations.