  We estimate the thin disk scale height of the Galactic population of L- &
T-dwarfs based on star counts from 15 deep parallel fields from the Hubble
Space Telescope. From these observations, we have identified 28 candidate L- &
T- dwarfs based on their (i'-z') color and morphology. By comparing these star
counts to a simple Galactic model, we estimate the scale height to be 350+-50
pc that is consistent with the increase in vertical scale with decreasing
stellar mass and is independent of reddening, color-magnitude limits, and other
Galactic parameters. With this refined measure, we predict that less than 10^9
M_{sol} of the Milky Way can be in the form L- & T- dwarfs, and confirm that
high-latitude, z~6 galaxy surveys which use the i'-band dropout technique are
97-100% free of L- & T- dwarf interlopers.
