The alkene 2,4-dimethyl-8-oxabicyclo[3.2.1]-oct-6-en-3-one (3) was converted to 1,3,10-trimethyl-8-oxabicyclo[5.3.0]-dec-3-ene-2,9-dione (7) and 1,3-dimethyl-8-oxabicyclo[5.3.0]-dec-3-ene-2,9-dione (8) with a 55% overall yield in both cases. Lactones (7) and (8) were converted in two steps to 1,3,4-trimethyl-13-methylene-6-oxatricyclo[8.3.0.0 3,7]-trideca-2,5,12-trione (12) (63%) and 1,3-dimethyl-13-methylene-6...