It has been observed for a plane-parallel resonator with a saturated medium that under certain conditions confined beams mainly concentrated near the axis are present. The experiments have been done with a sealed-off plane-parallel CO2 laser of one meter length and with an internal diameter of 20 mm. Without gain variations such a system is unstable because of thermal defocussing by the heated gas. But due to sufficiently high gain variations the beam converges nevertheless. Since the gain variation increases with decreasing reflectivity confined beams near the optical axis are only observed at sufficiently low reflectivity. The experiments were done with a totally reflecting mirror and an outcoupling mirror having a reflectivity of, respectively, 90%, 80%, 50%, and 36%. For the high reflectivities the outcoupled beam is mainly concentrated near the edge with irregular density distributions. For the low reflectivity the beam is more or less radially symmetric, concentrated near the axis having decreasing intensity with the distance from the axis. The behaviour can be understood by an analysis in which the constant and quadratic term of the complex propagation constant near the optical axis due to gain variations, dispersion and heat effects are taken into account.