  We report on the results of a survey for radial velocity variability in a
heterogeneous sample of very low-mass stars and brown dwarfs. One
distinguishing characteristic of the survey is its timespan, which allows an
overlap between spectroscopic binaries and those which can be found by high
angular-resolution imaging. We are able to place a new constraint on the total
binary fraction in these objects, which suggests that they are more likely the
result of extending the same processes at work at higher masses into this mass
range, rather than a distinct mode of formation. Our basic result is that there
are $6 \pm 2$ out of 53, or $11^{+0.07}_{-0.04}$% spectroscopic binaries in the
separation range 0-6 AU, nearly as many as resolved binaries. This leads to an
estimate of an upper limit of $26 \pm 10$% for the binary fraction of VLM
objects (it is an upper limit because of the possible overlap between the
spectroscopic and resolved populations). A reasonable estimate for the very
low-mass binary fraction is $20 - 25$%. We consider several possible separation
and frequency distributions, including the same one as found for GK stars, a
compressed version of that, a version of the compressed distribution truncated
at 15 AU, and a theoretical distribution which considers the evaporation of
small-N clusters. We conclude that the latter two bracket the observations,
which may mean that these systems form with intrinsically smaller separations
due to their smaller mass, and then are truncated due to their smaller binding
energy. We do not find support for the ``ejection hypothesis'' as their
dominant mode of formation, particularly in view of the similarity in the total
binary fraction compared with slightly more massive stars, and the difficulty
this mechanism has in producing numerous binary systems.
