  High resolution spectral observations of the polar EF Eridani obtained in a
low state with X-Shooter revealed narrow emission lines from the irradiated
secondary. The lines were most prominent in the near-IR Ca2-triplet, the more
intensive Halpha line had additional emission likely originating from an
accretion stream. The lines with a radial velocity amplitude, K2' = 385 +- 4
kmps, serve as tracer of the otherwise unseen companion. The mass function
implies a massive white dwarf with Mwd > 0.65 Msun at 3sigma confidence, and a
short distance to the binary, d ~ 111 pc (<145pc at 3sigma confidence). The
spectral energy distribution from the UV to the IR together with the high mass
ratio gives further strong evidence of EF Eri being a post period-minimum
object with M2 < 0.06 Msun
