Shear reversal is a smart rheological protocol allowing inspection of the contribution of the nonhydrodynamic contact forces between particles on the rheology of concentrated suspensions. In this paper, this protocol is applied to concentrated suspensions of rigid fibers dispersed in a Newtonian liquid at three aspect ratios ranging from 10 to 31 and various concentrations. When the shear direction is reversed, a low viscosity pseudoplateau is observed and we show that the value of the viscosity at pseudoplateau is close to the steady-state viscosity value expected for semidilute suspensions where the fibers interact mainly via hydrodynamic forces, while the contact interactions are released for a short time just after shear reversal. The low viscosity pseudoplateau is followed by a viscosity overshoot that is interpreted in terms of the interplay between contact interparticle interactions (that reappear at the end of the low viscosity plateau) and fiber reorientation. In particular, we show that the accumulated strain at which the overshoot occurs is controlled by a strain scale associated with the reconstruction of the contact network. After the viscosity overshoot, the viscosity decreases and reaches the steady value that it had before shear reversal. (C) 2019 The Society of Rheology.