Semantic relations are often signaled with prepositional or possessive marking—but extreme polysemy bedevils their analysis and automatic interpretation. We introduce a new annotation scheme, corpus, and task for the disambiguation of prepositions and possessives in English. Unlike previous approaches, our annotations are comprehensive with respect to types and tokens of these markers; use broadly applicable supersense classes rather than fine-grained dictionary definitions; unite prepositions and possessives under the same class inventory; and distinguish between a marker’s lexical contribution and the role it marks in the context of a predicate or scene. Strong interannotator agreement rates, as well as encouraging disambiguation results with established supervised methods, speak to the viability of the scheme and task.