Context. In recent years, infrared interferometry has revealed the presence of faint dusty circumstellar envelopes (CSE) around Cepheids. However the size, shape, chemical nature, and the interaction of the CSE with the star itself are still under investigation. The presence of a CSE might have an effect on the angular diameter estimates used in the interferometric Baade-Wesselink and surface-brightness methods of determining the distance of Cepheids. Aims. By studying Hα profiles as a function of the period, we investigate the permanent mass loss and the CSE around Cepheids. Our high spectral- and time-resolution data, combined with a very good S/N, will be useful in constraining future hydrodynamical models of Cepheids atmosphere and their close environment. Methods. We present HARPS �� high-resolution spectroscopy (R = 120 000) of eight galactic Cepheids: R Tra, S Cru, Y Sgr, β Dor, ζ Gem, RZ Vel, � Car, and RS Pup, providing a good period sampling (P = 3.39 d to P = 41.52 d). The Hα line profiles are described for all stars using a 2D (wavelength versus pulsation phase) representation. For each star, an average spectral line profile is derived, together with its first moment (γ-velocity) and its asymmetry (γ-asymmetry). Results. Short-period Cepheids show Hα line profiles following the pulsating envelope of the star, while long-period Cepheids show very complex line profiles and, in particular, large asymmetries. We find a new relationship between the period of Cepheids and their γ-velocities and -asymmetries. These results may be related to the dynamical structure of the atmosphere and to a permanent mass