The orientation state of a dilute suspension of rigid, axisymmetric particles subjected to the sudden inception of simple shearing flow in the presence of small Brownian couples is investigated experimentally. In contrast to mechanical rheometric methods, the experimental technique, a recently developed optical method based on conservative linear dichroism (Frattini & Fuller 1984), provides a direct probe of the constituent particle dynamics. The average particle orientation direction projected into the shear plane and the average degree of alignment about that direction are measured as functions of time for Péclet numbers, $\dot{\gamma}/D_{\rm r}$, ranging from 20 to 200. Data are presented for dilute glycerol/water suspensions of two types of particles: disk-like bentonite clay and rod-like synthetic akaganeite (βFeOOH). The data provide, for the first time, an experimental basis with which the closure approximation required for solution of the evolution equation for 〈u,u〉, the second moment of the particle orientation distribution, may be critically evaluated in shearing flows. Two closures are examined: the ad hoc but often-used pre-averaging closure, and the first-order closure suggested by Hinch & Leal (1976). The latter results in a more accurate fit of the data. Finally, new experimental observations of the effect of particle size polydispersity are reported for the orientation relaxation following sudden cessation of steady simple shear at moderately high Péclet number.