When the probability of a single member of a set of mutually exclusive and exhaustive possibilities is judged, its alternatives are evaluated as a composite "residual" hypothesis. Support theory (Rottenstreich & Tversky, 1997; Tversky & Koehler, 1994) implies that the process of packing alternatives together in the residual reduces the perceived evidential support for the set of alternatives and consequently inflates the judged probability of the focal hypothesis. Previous work has investigated the global weights that determine the extent to which the overall evidential support for the alternatives is discounted by this packing operation (Koehler, Brenner, & Tversky, 1997). In the present investigation, we analyze this issue in greater detail, examining the local weights that measure the specific contribution of each component hypothesis included implicitly in the residual. We describe a procedure for estimating local weights and introduce a set of plausible properties that impose systematic ordinal relationships among local weights. Results from four experiments testing these properties are reported, and a local-weight model is developed that accounts for nearly all of the variance in the probability judgments in these empirical tests. Local weights appear to be sensitive both to the individual component with which they are associated and to the residual hypothesis in which the component resides.