We present a deep optical survey of Uranus' Hill sphere for small satellites. The Subaru 8-m telescope was used to survey about 3.5 square degrees with a 50% detection efficiency at limiting red magnitude m = 26.1 mag. This magnitude corresponds to objects that are about 7 km in radius (assuming an albedo of 0.04). We detected (without prior knowledge of their positions) all previously known outer satellites and discovered two new irregular satellites (S/2001 U2 and S/2003 U3). The two inner satellites Titania and Oberon were also detected. One of the newly discovered satellites (S/2003 U3) is the first known irregular prograde of the planet. The population, size distribution and orbital parameters of Uranus' irregular satellites are remarkably similar to the irregular satellites of gas giant Jupiter. Both have shallow size distributions (power law indices q~2 for radii > 7 km) with no correlation between the sizes of the satellites and their orbital parameters. However, unlike those of Jupiter, Uranus' irregular satellites do not appear to occupy tight distinct dynamical groups in semi-major axis versus inclination phase space. Two groupings in semi-major axis versus eccentricity phase space appear to be statistically significant.

10 Figures (2 color), 3 Tables, to appear in AJ January 2005