<p>This paper characterizes three new rules for allocating resources in bilateral conflicting claims problems. These rules incorporate lower and upper exclusion thresholds that determine whether an individual is excluded from initial gains or losses. After prioritizing individuals according to these thresholds, the first rule assigns awards proportionally to them. The other two rules use weighted proportional divisions to ensure equal treatment of gains and losses once an exclusion threshold is reached. By incorporating exclusion thresholds into bilateral claims problems, our framework extends the class of division rules for resource allocation in contexts where symmetry is not appropriate due to legal and policy considerations.</p>