  We present predictions for the surface density of ultracool dwarfs (with
spectral types M8-T8) for a host of deep fields that are likely to be observed
with the James Webb Space Telescope. Based on simple thin and thick/thin disk
(exponential) models, we show the typical distance modulus is mu~9.8 mag, which
at high Galactic latitude is 5log(2 z_scl)-5. Since this is a property of the
density distribution of an exponential disk, it is independent of spectral type
or stellar sample. Using the published estimates of the ultracool dwarf
luminosity function, we show that their number counts typically peak around
J~24 mag with a total surface density of Sigma ~ 0.3 arcmin^-2, but with a
strong dependence on galactic coordinate and spectral type. Owing to the
exponential shape of the disk, the ultracool dwarfs are very rare at faint
magnitudes (J>~27 mag), with typical densities of Sigma~0.005 arcmin^-2 (or
~20% of the total contribution within the field). Therefore in the very narrow
and deep fields, we predict there are only a few ultracool dwarfs, and hence
these stars are likely not a severe contaminant in searches for high-redshift
galaxies. Furthermore the ultracool dwarfs are expected to be considerably
brighter than the high-redshift galaxies, so samples near the faint-end of the
high-redshift galaxy population will be the purest. We present the star-count
formalism in a simplified way so that observers may easily predict the number
of stars for their conditions (field, depth, wavelength, etc.).
