  We discuss consistent power counting for integrating soft and collinear
degrees of freedom over arbitrary regions of phase space in the soft-collinear
effective theory (SCET), and illustrate our results at one loop with several
jet algorithms: JADE, Sterman-Weinberg and k_T. Consistently applying SCET
power-counting in phase space, along with non-trivial zero-bin subtractions,
prevents double-counting of final states. The resulting phase-space integrals
over soft and collinear regions are individually ultraviolet divergent, but the
phase-space ultraviolet divergences cancel in the sum. Whether the soft and
collinear contributions are individually infrared safe depends on the jet
definition. We show that while this is true at one loop for JADE and
Sterman-Weinberg, the k_T algorithm does not factorize into individually
infrared safe soft and collinear pieces in dimensional regularization. We point
out that this statement depends on the ultraviolet regulator, and that in a
cutoff scheme the soft functions are infrared safe.
