 If impossible worlds display different degrees of logical structure (or lack thereof), it may make sense to order them. A natural way to do this is via an extension of the traditional “closeness” relations between possible worlds. How to spell out the ordering in detail, though, is far from straightforward. Within standard conditional logics, and in the treatment of counterfactual conditionals in terms of possible worlds due to Robert Stalnaker (1968) and David Lewis (1973), worlds stand in similarity relations; and similarity comes in degrees. This is usually represented by having each possible world, \(w\), come with a system of “spheres”. If \(W\) is the set of all worlds, let \(\$\) be a function from worlds to sets of subsets of \(W\), so that \(\$w = \{S_1, S_2 , \ldots \}\), with \(w \in S_1 \subseteq S_2 \subseteq \ldots = W\). Worlds within a given sphere \(S_i\) are more similar to \(w\) than worlds outside it.