This paper deals with the problem of "of"-possessives (e.g., "the cover of a book") that antecede donkey pronouns. Donkey sentences with "of"-possessive antecedents (e.g., "if the cover of a book is missing, someone unethical must have removed it") present a complication for current theories of donkey pronouns: the immediate antecedent of the pronoun ("the cover of a book") is definite, but it is the buried indefinite possessor ("a book") that triggers a quantificational variability effect in the antecedent. Current theories consistently rely on the indefinite determiner being the head of the antecedent, and therefore make the wrong predictions about "of"-possessives. The paper discusses the problem from the perspective of both E-type/D-type theories of donkey pronouns, and dynamic theories, and develops a compositional dynamic analaysis of "of"-possessive antecedents. The analysis involves local accommodation of a familiarity presupposition during composition; a constraint on accommodation keyed on the presence of a salient relation introduced by the relational noun head permits accommodation in "of"-possessives but not with definite descriptions generally.