[en] Eight more thermal pulses have been calculated for a 7 M/sub sun/ model star with a carbon-oxygen core of mass 0.95--0.96 M/sub sun/. From the 10th to the 18th pulse, the maximum helium-burning luminosity, the maximum temperature at the base of the convective shell, and the amount of matter containing fresh carbon that is dredged up by the convective envelope increase, respectively, from 1.6 x 10⁶ L/sub sun/, 286 x 10⁶ K, and 3.5 x 10^-5 M/sub sun/ to 5.5 x 10⁶ L/sub sun/, 310 x 10⁶ K, and approx.4.0 x 10^-4 M/sub sun/. The mass of carbon-rich matter dredged up near the end of the 18th pulse is over one-third of the mass through which the hydrogen-burning shell has advanced during the preceding interpulse phase.It is shown that the failure of the outer edge of the convective shell to reach the hydrogen-helium interface is a consequence of an ''entropy barrier'' set up through this interface during the interpulse phase and that radiation pressure is the dominant contributor to the magnitude of this barrier. Similarly, the dredging-up phenomenon can be understood in terms of widely different rates of entropy change on either side of the hydrogen-helium interface.Finally, it is shown that, during the dredging-up process, a discontinuity in the radiative gradient at the base of the envelope convective region may lead to overshoot, one consequence of which is the formation of ²²Ne in a convective shell at an abundance exceeding the abundance of CNO elements at the surface. This has ramifications for the production of light s-process elements (²³Na→³⁰Si) in Population II stars of intermediate mass during the early history of the Galaxy