Although in principle states can bargain over the entire extent of their combined territory, we observe historically that states bargain within far more limited confines defined by well-bounded claims. We argue that this observation stems from the fact that states generally have limited territorial aims due either to limited benefits of obtaining additional territory and/or the costs of absorbing and controlling new territories and their inhabitants. Using a formal model, we show that introducing states with limited aims over territory has strategic implications for bargaining that have not been appreciated in canonical models that do not consider heterogeneity in state preferences. Whereas traditional models generally imply that small demands undermine the credibility of a challenger's threat, the existence of states with limited territorial aims makes limited demands credible, effective, and stable in the face of shocks to relative power. We then employ geospatial data on the geographic extent of territorial disputes in the period 1947–2000 to establish two results: the size of claims is weakly related to the relative power of disputants and unaffected by dramatic changes in power, and smaller claims are associated with a higher probability that the challenger will receive any concession.