  The eclipsing polar CSS081231 turned bright (V_max ~ 14.5) in late 2008 and
was subsequently observed intensively with small and medium-sized telescopes. A
homogeneous analysis of this comprehensive dataset comprising 109 eclipse
epochs is presented and a linear ephemeris covering the five years of
observations, about 24000 orbital cycles, is derived. Formally this sets rather
tight constraints on the mass of a hypothetical circumbinary planet, M_pl <= 2
M_Jup. This preliminary result needs consolidation by long-term monitoring of
the source. The eclipse lasts 433.08 +- 0.65 s, and the orbital inclination is
found to be i=79.3 - 83.7 degrees. The centre of the bright phase displays
accretion-rate dependent azimuthal shifts. No accretion geometry is found that
explains all observational constraints, suggesting a complex accretion geometry
with possible pole switches and a likely non-dipolar field geometry.
