This study describes the transition between the quasi-static and the viscous regimes of shearing of thin layers of spheres in a viscous fluid at high solid loadings. Experiments were conducted in a Couette-type shear cell in two complementary modes : (a) constant particle normal stress, variable solid fraction and (b) constant solid fraction, variable particle normal stress. During steady shearing under the constraint of constant solid fraction, transition from a strain rate independent stress to one with a linearly dependent behavior was found to occur with a local minimum in the stresses with respect to strain rate; correspondingly, the solid fraction assumed a maximum with respect to strain rate under conditions of constant normal stress. These are the first observations of such a phenomenon, which we call viscous compaction. At sufficiently high strain rates, the mixture exhibited a linear Newtonian-like scaling between strain rate and both shear and normal stresses. These measurements of normal stress are the first since those of Bagnold.