  In magnetic multilayers, a dc current induces a spin precession above a
certain critical current. Drive torques responsible for this can be calculated
from the spin accumulation $\bar{\Delta\mu}$. Existing calculations of
$\bar{\Delta\mu}$ assume a uniform cross section of conductors. But most
multilayer samples are pillars with current leads flaring out immediately to a
much wider cross-section area than that of the pillar itself. We write
spin-diffusion equations of a form valid for variable cross section, and solve
the case of flat electrodes with radial current distribution perpendicular to
the axis of the pillar. Because of the increased volume available for
conduction-electron spin relaxation in such leads, $\bar{\Delta\mu}$ is reduced
in the pillar by at least a factor of 2 below its value for uniform cross
section, for given current density in the pillar. Also, $\bar{\Delta\mu}$ and
the critical current density for spin precession become nearly independent of
the thickness of the pinned magnetic layer, and more dependent on the thickness
of the spacer, in better agreement with measurements by Albert et al. (2002).
