We propose an analysis that derives Cinque's (2005) typology of linear orders involving a demonstrative, numeral, adjective, and noun through four Optimality Theory constraints requiring leftward alignment of these items. We show that remnant movement is ungrammatical whenever it produces universally suboptimal alignments, compared with remnant-movement-free structures. Any movement is permitted, but only the best alignment configurations surface as grammatical. We also show that Cinque's original analysis must encode the structural derivations of all attested orders as parametric values of the associated languages. Our analysis need not make similar structural stipulations, as the different attested structures emerge from constraint reranking.