Maps in the CO (J = 2-1) line of the southern H II region complexes Carina Nebula and G333.6-0.2/RCW 106 are presented and discussed. Results for the Carina Nebula indicate a complicated spatial structure; an extended molecular cloud appears to be wrapped partly around the brightest parts of the H II region (Car I and Car II). The situation in Carina is consistent with a model for sequential star formation proposed by Elmergreen and Lada (1977). At the positions of the other sources observed, a giant molecular complex, at least 75 pc long and 20 pc wide, is found. The complex consists of at least four large clouds and coincides accurately with a distinct minimum in the H I distribution.