Context : A 10.24 days Neptune-mass planet was recently announced to orbit the nearby M2 dwarf Gl 176 , based on 28 radial velocities measured with the HRS spectrograph on the Hobby-Heberly Telescope . Aims : Methods : We obtained 57 radial velocities of Gl 176 with the ESO 3.6m telescope and the HARPS spectrograph , which is known for its sub-m/s stability . The median photon-noise standard error of our measurements is 1.1 m/s , significantly lower than the 4.7 m/s of the HET velocities , and the 4 years period over which they were obtained has much overlap with the epochs of the HET measurements . Results : The HARPS measurements show no evidence for a signal at the period of the putative HET planet , suggesting that its detection was spurious . We do find , on the other hand , strong evidence for a lower mass 8.4 M _ { Earth } planet , in a quasi-circular orbit and at the different period of 8.78 days . The host star has moderate magnetic activity and rotates on a 39-days period , which we confirm through modulation of both contemporaneous photometry and chromospheric indices . We detect that period as well in the radial velocities , but it is well removed from the orbital period and no cause for confusion . Conclusions : This new detection of a super-Earth ( 2 M _ { Earth } <  M sin ( i )  <  10 M _ { Earth } ) around an M dwarf adds to the growing evidence that such planets are common around very low mass stars : a third of the 20 known planets with M sin ( i )  <  0.1 M _ { Jup } and 3 of the 7 known planets with M sin ( i )  <  10 M _ { Earth } orbit an M dwarf , in contrast to just 4 of the \sim 300 known Jupiter-mass planets .