Cutter Interference(or part surface gouging) is one of the most critical problems in NC machining of sculptured surfaces. Presented in this paper is and algorithmic procedure that converts CC data obtained from a compound surface(several surfaces without topological relationship) into interference-free CL data. The interference handling procedure consists of following steps: (1) Z-map model is constructed from input surfaces. (2) Interference sources are detected using local properties of the sources. (3) Interference regions are completely identified based on global tests for neighboring CC points of the interference sources (4) Cutter paths are reconstructed after removing the CC data in interference regions, while avoiding any new interferences.