  We have searched a 2010 archival data set from the Canada-France-Hawaii
Telescope for very small (km-scale) irregular moons of Jupiter in order to
constrain the size distribution of these moons down to radii of $\sim 400$~m,
discovering 52 objects which are moving with Jupiter-like on-sky rates and are
nearly certainly irregular moons. The four brightest detections, and seven in
total, were all then linked to known jovian moons. Extrapolating our
characterized detections (those down to magnitude $m_r=25.7$) to the entire
retrograde circum-jovian population, we estimate the population of radius
$>0.4$~km moons to be 600 (within a factor of 2). At the faintest magnitudes we
find a relatively shallow luminosity function of exponential index $\alpha=
0.29 \pm 0.15$, corresponding to a differential diameter power law of index
$q\simeq 2.5$.
