  An algorithm is presented in which the Colour-Dipole Cascade Model as
implemented in the Ariadne program is corrected to match the fixed order
tree-level matrix elements for e+e- -> n jets. The result is a full parton
level generator for e+e- annihilation where the generated states are correct on
tree-level to fixed order in alpha_S and to all orders with modified leading
logarithmic (MLLA) accuracy. In this paper, matrix elements are used up to
second order in alpha_S, but the scheme is applicable also for higher orders.
An improvement to also include exact virtual corrections to fixed order is
suggested and the possibility to extend the scheme to hadronic collisions is
discussed.
