Dispersion relations for Alfven surface waves in a cylindrical plasma have previously been obtained by assuming that the plasma is separated from a conducting wall by a vacuum gap. The authors examine the effect of replacing the vacuum layer by a region of low density plasma. The low density region has little effect on negative m surface waves, but introduces an ion cyclotron resonance and a waveguide cut-off for positive m modes. These effects are associated with the fact that positive m modes are left hand polarised near the plasma edge. Dispersion relations for stepped and parabolic density profiles are examined. A profile with N discrete steps and a vacuum boundary supports a discrete spectrum of N+1 first radial modes. When N is large, these modes can be identified as N localised torsional wave modes plus one surface wave mode.