  [abridged] We present MMT/Megacam imaging in Sloan $g$ and $r$ of the
extremely low luminosity Bo\"otes II Milky Way companion. We use a bootstrap
approach to perform robust measurements of, and uncertainties on, Bo\"otes II's
distance, luminosity, size, and morphology. We show that Bo\"otes II's stellar
population is old and metal-poor ([Fe/H] $\lta$ -2). Assuming a stellar
population like that of M92, Bo\"otes II is at a distance of 42 $\pm$ 2 kpc,
closer than the initial published estimate of 60 $\pm$ 10 kpc. This distance
revision, combined with a more robust measurement of Bo\"otes II's structure
with a Plummer model (exponential model) results in a more compact half-light
size of $r_h\simeq 36 (33) \pm 9 (10)$ pc and lower luminosity of
$M_V\simeq-2.4 (-2.2) \pm 0.7 (0.7)$ mag. This revised size and luminosity move
Bo\"otes II into a region of size-luminosity space not previously known to be
occupied by old stellar populations, but also occupied by the recently
discovered Milky Way satellites Willman 1 and SEGUE 1. We show that the
apparently distorted morphology of Bo\"otes II is not statistically significant
given the present data. We use a tidal argument to support a scenario where
Bo\"otes II is a dwarf galaxy (dark matter dominated) rather than a globular
cluster (not dark matter dominated). However, we can not rule out that Bo\"otes
II is a star cluster on the verge of disruption, such as Palomar 5.
