A parallel version of an indirect approach for meshing composite surfaces - also called multiface models - is recalled. In practice, however, this methodology may be inefficient because the memory management of most existing Computer Aided Design (CAD) systems uses caches to save information. Two solutions are presented, referred to as the Pirate approach and the Discrete approach. In the first approach, the Pirate library can be efficiently called in parallel since no caching is used for the storage or evaluation of geometric primitives. In the second approach, the CAD environment is replaced by internal procedures interpolating a discrete geometric support. In both cases, performance measurements are presented and show significant gains.