  We report on the results from a five-night campaign of high-speed
spectroscopy of the 17-minute binary AM Canum Venaticorum, obtained with the
4.2-m William Herschel Telescope on La Palma.
  We derive a mass ratio q=0.18+/-0.01 for AM CVn, which is significantly
higher than the value found in previous, less direct measurements. We discuss
the implications for AM CVn's evolutionary history and show that a helium star
progenitor scenario is strongly favoured. We further discuss the implications
for the interpretation of AM CVn's superhump behaviour, and for the
detectability of its gravitational-wave signal with LISA.
  Finally, we test the predictions of an eccentric, precessing disc that are
based on AM CVn's observed superhump behaviour. We limit the effective
eccentricity in the outermost part of the disc, where the resonances that drive
the eccentricity are thought to occur, to e=0.04+/-0.01, which is smaller than
previous models indicated.
