  We analyse high-time-resolution spectroscopy of the AM CVn stars HP Librae
and V803 Centauri, taken with the New Technology Telescope (NTT) and the Very
Large Telescope (VLT) of the European Southern Observatory, Chile.
  We present evidence that the literature value for V803 Cen's orbital period
is incorrect, based on an observed `S-wave' in the binary's spectrogram. We
measure a spectroscopic period P=1596.4+/-1.2s of the S-wave feature, which is
significantly shorter than the 1611-second periods found in previous
photometric studies. We conclude that the latter period likely represents a
`superhump'. If one assumes that our S-wave period is the orbital period, V803
Cen's mass ratio can be expected to be much less extreme than previously
thought, at q~0.07 rather than q~0.016. This relaxes the constraints on the
masses of the components considerably: the donor star does then not need to be
fully degenerate, and the mass of the accreting white dwarf no longer has to be
very close to the Chandrasekhar limit.
  For HP Lib, we similarly measure a spectroscopic period P=1102.8+/-0.2s. This
supports the identification of HP Lib's photometric periods found in the
literature, and the constraints upon the masses derived from them.
