  We present the discovery of four new long-period planets within the HARPS
high-precision sample: \object{HD137388}b ($M\sin{i}$ = 0.22 $M_J$),
\object{HD204941}b ($M\sin{i}$ = 0.27 $M_J$), \object{HD7199}b ($M\sin{i}$ =
0.29 $M_J$), \object{HD7449}b ($M\sin{i}$ = 1.04 $M_J$). A long-period
companion, probably a second planet, is also found orbiting HD7449. Planets
around HD137388, HD204941, and HD7199 have rather low eccentricities (less than
0.4) relative to the 0.82 eccentricity of HD7449b. {All these planets were
discovered even though their hosting stars have clear signs of activity.
Solar-like magnetic cycles, characterized by long-term activity variations, can
be seen for HD137388, HD204941 and HD7199, whereas the measurements of HD7449
reveal a short-term activity variation, most probably induced by magnetic
features on the stellar surface. We confirm that magnetic cycles induce a
long-term radial velocity variation and propose a method to reduce considerably
the associated noise.} The procedure consists of fitting the activity index and
applying the same solution to the radial velocities because a linear
correlation between the activity index and the radial velocity is found. Tested
on HD137388, HD204941, and HD7199, this correction reduces considerably the
stellar noise induced by magnetic cycles and allows us to derive precisely the
orbital parameters of planetary companions.
