[abridged] We present MMT/Megacam imaging in Sloan $g$ and $r$ of the extremely low luminosity Bo��tes II Milky Way companion. We use a bootstrap approach to perform robust measurements of, and uncertainties on, Bo��tes II's distance, luminosity, size, and morphology. We show that Bo��tes II's stellar population is old and metal-poor ([Fe/H] $\lta$ -2). Assuming a stellar population like that of M92, Bo��tes 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��tes 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��tes 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��tes II is not statistically significant given the present data. We use a tidal argument to support a scenario where Bo��tes 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��tes II is a star cluster on the verge of disruption, such as Palomar 5.

10 pages, 8 figures. ApJ accepted. Conclusions are unchanged, but content and figures have changed substantively in this accepted version