THIS PAPER CORRECTS AN ERROR IN MY EARLIER PAPER, "CONCEPTS OF SUPERVENIENCE" ("PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH", VOLUME 45, 1984), AND PRESENTS FURTHER MATERIAL ON SUPERVENIENCE. THE ERROR IS THE CLAIM THAT "GLOBAL" SUPERVENIENCE ENTAILS "STRONG" SUPERVENIENCE. HOWEVER, IT IS ARGUED THAT THIS FAILURE OF ENTAILMENT ONLY GOES TO SHOW THE INADEQUACY OF GLOBAL SUPERVENIENCE AS AN EXPLICATION OF "DEPENDENCY" OR "DETERMINATION" RELATION, AND, IN PARTICULAR, THAT MATERIALISM FORMULATED IN TERMS OF GLOBAL SUPERVENIENCE APPEARS TOO WEAK. (IT IS POINTED OUT, AMONG (...) OTHER THINGS, THAT GLOBAL SUPERVENIENCE DOES NOT ENTAIL "WEAK" SUPERVENIENCE). A STRONGER FORM OF GLOBAL SUPERVENIENCE, BASED ON "SIMILARITY" RATHER THAN "INDISCERNIBILITY" BETWEEN WORLDS, IS FORMULATED AND BRIEFLY DISCUSSED. (shrink)