Under an "offer of settlement" rule, a party to a lawsuit may make a special offer to settle with the other party, such that if the other party rejects this offer, then this offer (unlike an ordinary offer) becomes part of the record in the case and may affect the allocation of litigation costs. Specifically, if the parties litigate to judgment, then the allocation of litigation costs may depend on how the judgment compares with the special offer. This paper develops a model of bargaining under offer-of settlement rules that can be used to analyze the effect that such rules have on the terms of settlement. The analysis first sets forth a general principle that identifies the settlement amount under any such rule. We then apply this principle to derive the settlement terms under the most important of these rules, and we identify a large set of seemingly different rules that produce identical settlements. Our results have both positive and normative implications.