 Lewis’s possibilist realism faces the problem of specifying non-actual possible objects. Take Vulcan, the innermost planet between Sun and Mercury erroneously believed to exist by some astronomers in the nineteenth century, when the universe was assumed to be Newtonian. Vulcan is not actually between Sun and Mercury or actually anywhere at all. Vulcan also does not actually have any mass, shape, or chemical composition. Still it is possible that Vulcan be a unique planet between Sun and Mercury and have a particular mass m, a particular shape s, and a particular chemical composition c. Or so it seems. It is also possible, it seems, that Vulcan be a unique planet between Sun and Mercury and have a slightly different particular mass m′, a slightly different particular shape s′, and a slightly different particular chemical composition c′, where the slight differences in question lie within the range of deviations the original astronomers would have tolerated. So at some possible world w Vulcan is a unique planet between Sun and Mercury and has m, s, and c, and at some possible world w′ Vulcan is a unique planet between Sun and Mercury and has m′, s′, and c′. Clearly w and w′ are different worlds. On Lewis’s theory, every possible object exists at only one world. So either the planet in question at w is not Vulcan or the planet at w′ is not Vulcan. Whichever planet that is not Vulcan is Vulcan’s counterpart at best. Is either planet Vulcan? If so, which one? If neither is, where is Vulcan? What possible world hosts Vulcan? There seems to be no non-arbitrary way to answer these questions within Lewis’s theory.