  We consider essential mechanisms for orbit-shrinkage or "hardening" of
compact binaries in globular clusters to the point of Roche-lobe contact and
X-ray emission phase, focussing on the process of collisional hardening due to
encounters between binaries and single stars in the cluster core. The interplay
between this kind of hardening and that due to emission of gravitational
radiation produces a characteristic scaling of the orbit-shrinkage time with
the single-star binary encounter rate $\gamma$ in the cluster which we
introduce, clarify, and explore. We investigate possible effects of this
scaling on populations of X-ray binaries in globular clusters within the
framework of a simple "toy" scheme for describing the evolution of pre-X-ray
binaries in globular clusters. We find the expected qualitative trends
sufficiently supported by data on X-ray binaries in galactic globular clusters
to encourage us toward a more quantitative study.
