The linear stability of the mixing layer of a fiber suspension is considered using a model based on moments of the orientation distribution function. This investigation follows a previous paper that examined high Reynolds number flows of large aspect ratio fibers in an exclusively planar orientation [J. Fluid Mech. 404 (2000) 179]. The objective of this study is to determine the dependence of the results of the stability analysis on the nature of the closure approximation, and to address the important issue of the effects of fiber off-plane orientation. The analysis is undertaken for three different cases: a planar orientation distribution using the natural and the hybrid closure approximations, and a three-dimensional orientation distribution using the hybrid closure approximation. It is found that for a planar orientation, the trends towards decreasing the flow instability are similar in the case of the natural and hybrid closure approximations, even though the former leads to a less unstable flow. Accounting for off-plane orientation leads to substantially different instability characteristics. In this case, the flow is considerably less unstable than its planar counterpart. An analysis of the affects of the fiber on the flow dynamics shows fundamental differences between the three cases. In the case of a planar orientation the shear stress disturbances tend to enhance the flow stability while the normal stress disturbances act towards increasing the instability. On the other hand, for a three-dimensional orientation both the shear and normal stress components of the stress disturbance play a stabilizing role and oppose the destabilizing role of the convective term. This fundamental difference between the planar and three-dimensional configurations is explained in terms of the differences in the resulting orientation distributions.