  We construct an improved implementation for combining
transverse-momentum-dependent (TMD) factorization and collinear factorization.
TMD factorization is suitable for low transverse momentum physics, while
collinear factorization is suitable for high transverse momenta and for a cross
section integrated over transverse momentum. The result is a modified version
of the standard $W+Y$ prescription traditionally used in the
Collins-Soper-Sterman (CSS) formalism and related approaches. We further argue
that questions regarding the shape and $Q$-dependence of the cross sections at
lower $Q$ are largely governed by the matching to the $Y$-term.
