  We collect well-measured opposition surge properties for many icy bodies
orbiting the Sun (mostly from our own observations) plus for many icy moons,
resulting in a data base of surface and orbital properties for 52 icy bodies.
(1) We put forward four criteria for determining whether the surge is being
dominated by shadow hiding (SH) or coherent backscattering (CB) based on
readily measured quantities. The CB surge mechanism dominates if the surge is
color dependent, the phase curve is steeper than 0.04 mag/deg, the phase curve
shape matches the CB model of Hapke, or if the albedo is higher than roughly
40%. (2) We find that virtually all of our sample have their phase curves
dominated by CB at low phase angles. (3) We present a graphical method to
determine the Hapke surge parameters B_C0 and h_C. (4) The Kuiper Belt Objects
(KBOs) and Centaurs have relatively high surge amplitudes, B_C0 > ~0.5 and
widths with h_C ~ 3 deg. (5) We find highly significant but loose correlations
between surge properties and the colors, albedos, and inclinations. We
interpret this as young surfaces tending to have low surge slopes, high albedo,
and gray colors. (6) Nereid has its surface properties similar to other icy
moons and greatly different from KBOs and Centaurs, so we conclude that Nereid
is likely a nearly-ejected inner Neptunian moon rather than a captured KBO.
