  In this article, we show that, for any compact 3-manifold, there is a $C^{1}$
volume-minimizing one-dimensional foliation. More generally, we show the
existence of mass-minimizing rectifiable sections of sphere bundles without
isolated "pole points" in the base manifold. This same analysis is used to show
that the examples, due to Sharon Pedersen, of potentially volume-minimizing
rectifiable sections (rectifiable foliations) of the unit tangent bundle to
$S^{2n+1}$ are not, in fact, volume minimizing.
