We derive the structural parameters of the recently discovered very low luminosity Milky Way satellites through a Maximum Likelihood algorithm applied to SDSS data. For each satellite, even when only a few tens of stars are available down to the SDSS flux limit, the algorithm yields robust estimates and errors for the centroid, position angle, ellipticity, exponential half-light radius and number of member stars. This latter parameter is then used in conjunction with stellar population models of the satellites to derive their absolute magnitudes and stellar masses, accounting for `CMD shot-noise. We find that faint systems are somewhat more elliptical than initially found and ascribe that to the previous use of smoothed maps which can be dominated by the smoothing kernel. As a result, the faintest half of the Milky Way dwarf galaxies (M_V>-7.5) is significantly (4-sigma) flatter (e=0.47+/-0.03) than its brightest half (M_V<-7.5, e=0.32+/-0.02). From our best models, we also investigate whether the seemingly distorted shape of the satellites, often taken to be a sign of tidal distortion, can be quantified. We find that, except for tentative evidence of distortion in CVnI and UMaII, these can be completely accounted for by Poisson scatter in the sparsely sampled systems. We consider three scenarios that could explain the rather elongated shape of faint satellites: rotation supported systems, stars following the shape of more triaxial dark matter subhalos, or elongation due to tidal interaction with the Milky Way. Although none of these is entirely satisfactory, the last one appears the least problematic, but warrants much deeper observations to track evidence of such tidal interaction.
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