This article argues that inversion of the subject and auxiliary in Eng
lish matrix questions and elsewhere is the effect of a violable optima
lity-theoretic constraint that requires head positions to be filled. W
hen no other auxiliary is available, do-support occurs to satisfy this
constraint, resulting in the presence of an expletive verb. When a hi
gher-ranked constraint prohibits inversion, no inversion or do-support
is found. The argument is then extended to cases where the complement
izer that is obligatory, which are shown to offer best satisfaction of
the proposed set of violable constraints.