  CoRoT-7 is an 11th magnitude K-star whose light curve shows transits with
depth of 0.3 mmag and a period of 0.854 d, superimposed on variability at the
1% level, due to the modulation of evolving active regions with the star's 23 d
rotation period. In this paper, we revisit the published HARPS radial velocity
measurements of the object, which were previously used to estimate the
companion mass, but have been the subject of ongoing debate.
  We build a realistic model of the star's activity during the HARPS
observations, by fitting simultaneously the line width and the line bisector,
and use it to evaluate the contribution of activity to the RV variations. The
data show clear evidence of errors above the level of the formal uncertainties,
which are accounted for either by activity, nor by any plausible planet model,
and which increase rapidly with decreasing signal-to-noise of the spectra. We
cite evidence of similar systematics in mid-SNR spectra of other targets
obtained with HARPS and other high-precision RV spectrographs, and discuss
possible sources. Allowing for these, we re-evaluate the semi-amplitude of the
CoRoT-7b signal, finding Kb=1.6 +-1.3 m/s, a tentative detection with a much
reduced significance (1.2-sigma) compared to previous estimates. We also argue
that the combined presence of activity and additional errors preclude a
meaningful search for additional low-mass companions, despite previous claims
to the contrary.
  Our analysis points to a lower density for CoRoT-7b, the 1-sigma mass range
spanning 1-4 MEarth, allowing for a wide range of bulk compositions. In
particular, an ice-rich composition is compatible with the RV constraints. This
study highlights the importance of a realistic treatment of both activity and
uncertainties, particularly in the medium signal-to-noise ratio regime, which
applies to most small planet candidates from CoRoT and Kepler.
