We present the analysis of the entire HARPS observations of three stars that host planetary systems: HD 1461, HD 40307, and HD 204313. The data set spans eight years and contains more than 200 nightly averaged velocity measurements for each star. This means that it is sensitive to both long-period and low-mass planets and also to the effects induced by stellar activity cycles. We modelled the data using Keplerian functions that correspond to planetary candidates and included the short- and long-term effects of magnetic activity. A Bayesian approach was taken both for the data modelling, which allowed us to include information from activity proxies such as log R'HK in the velocity modelling, and for the model selection, which permitted determining the number of significant signals in the system. The Bayesian model comparison overcomes the limitations inherent to the traditional periodogram analysis. We report an additional super-Earth planet in the HD 1461 system. Four out of the six planets previously reported for HD 40307 are confirmed and characterised. We discuss the remaining two proposed signals. In particular, we show that when the systematic uncertainty associated with the techniques for estimating model probabilities are taken into account, the current data are not conclusive concerning the existence of the habitable-zone candidate HD 40307 g. We also fully characterise the Neptune-mass planet that orbits HD 204313 in 34.9 days. Based on observations made with the HARPS instrument on the ESO 3.6 m telescope at La Silla Observatory under the GTO programme ID 072.C-0488, and its continuation programmes ID 183.C-0972, 091.C-0936, and 192.C-0852.Full Tables 3, 6, and 10 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/585/A134