This article discusses three asymmetries in ditransitives—quantifier scope, nominalizations, and idioms—and argues that an asymmetric theory like that advocated by Marantz (1993) and Bruening (2001) is correct. A symmetric theory like that proposed by Harley (1997, 2002) cannot account for the asymmetries. The article also proposes a complete theory of idiom formation based on selection. It also proposes a formal semantics for double object constructions that includes a mechanism for composing complex predicates. This semantics can account for the different readings of again and other modifiers, and can also be extended to nonalternating verbs like deny, spare, envy, and cost, with correct predictions about their behavior.