For ambiguous sentences, traditional semantics construction produces large numbers of higher-order formulas, which must then be -reduced individually. Underspeciﬁed versions can produce compact descriptions of all readings, but it is not known how to perform -reduction on these descriptions. We show how to do this using -reduction constraints in the constraint language for -structures (CLLS). They are based on dominance constraints (Marcus et al., 1983; Rambow et al., 1995) and extend them with parallelism (Erk and Niehren, 2000) and binding constraints. .