  We carry out a new analysis of the published radial velocity data for the
planet-hosting star HD82943. We include the recent Keck/HIRES measurements as
well as the aged but much more numerous CORALIE data. We find that the CORALIE
radial velocity measurements are polluted by a systematic annual variation
which affected the robustness of many previous results. We show that after
purging this variation, the residuals still contain a clear signature of an
additional $\sim 1100$ days periodicity. The latter variation leaves
significant hints in all three independent radial velocity subsets that we
analysed: the CORALIE data, the Keck data acquired prior to a hardware upgrade,
and the Keck data taken after the upgrade.
  We mainly treat this variation as a signature of a third planet in the
system, although we cannot rule out other interpretations, such as long-term
stellar activity. We find it easy to naturally obtain a stable three-planet
radial-velocity fit close to the three-planet mean-motion resonance 1:2:5, with
the two main planets (those in the 1:2 resonance) in an aligned apsidal
corotation. The dynamical status of the third planet is still uncertain: it may
reside in as well as slightly out of the 5:2 resonance. We obtain the value of
$\sim 1075$ days for its orbital period and of $\sim 0.3 M_{\rm Jup}$ for its
minimum mass, while the eccentric parameters are uncertain.
