Context : The K2.5 dwarf HD 40307 has been reported to host three super-Earths . The system lacks massive planets and is therefore a potential candidate for having additional low-mass planetary companions . Aims : We re-derive Doppler measurements from public HARPS spectra of HD 40307 to confirm the significance of the reported signals using independent data analysis methods . We also investigate these measurements for additional low-amplitude signals . Methods : We used Bayesian analysis of our radial velocities to estimate the probability densities of different model parameters . We also estimated the relative probabilities of models with differing numbers of Keplerian signals and verified their significance using periodogram analyses . We investigated the relation of the detected signals with the chromospheric emission of the star . As previously reported for other objects , we found that radial velocity signals correlated with the S-index are strongly wavelength dependent . Results : We identify two additional clear signals with periods of 34 and 51 days , both corresponding to planet candidates with minimum masses a few times that of the Earth . An additional sixth candidate is initially found at a period of 320 days . However , this signal correlates strongly with the chromospheric emission from the star and is also strongly wavelength dependent . When analysing the red half of the spectra only , the five putative planetary signals are recovered together with a very significant periodicity at about 200 days . This signal has a similar amplitude as the other new signals reported in the current work and corresponds to a planet candidate with M \sin i \sim 7 M _ { \oplus } ( HD 40307 g ) . Conclusions : We show that Doppler measurements can be filtered for activity-induced signals if enough photons and a sufficient wavelength interval are available . If the signal corresponding to HD 40307 g is a genuine Doppler signal of planetary origin , this candidate planet might be capable of supporting liquid water on its surface according to the current definition of the liquid water habitable zone around a star and is not likely to suffer from tidal locking . Also , at an angular separation of \sim 46 mas , HD 40307 g would be a primary target for a future space-based direct-imaging mission .