This paper considers the syntax of 'reduced' unconditional adjuncts in English: 'partially' reduced unconditionals, consisting of a wh-predicate plus DP (e.g. "We must accept every student, no matter how low their grades"), and 'fully' reduced unconditionals consisting only of the wh-predicate (e.g. "We must accept every student, however untalented"). Especially in the latter case, it is tempting to analyze such cases as instances of sluicing, on a par with interrogative/question examples like "He's talented, but I don't know how talented". I show, however, that reduced unconditionals (at least in English) do not result from sluicing. Rather, following Culicover 1999, I argue that 'partially' reduced unconditionals involve a small clause consisting only of the subject and wh-marked predicate. 'Fully' reduced unconditionals do not result from ellipsis, but rather make use of a null pronoun in the subject position of the small clause, a pronoun which I argue shows the properties of little 'pro'. Reduced unconditionals in English therefore appear to be genuine cases of pseudosluicing (Merchant 1998). I also formulate a previously unremarked-upon descriptive generalization concerning reduced unconditionals: one of the clauses in a reduced unconditional construction must contain a (possibly covert) E-type pronoun, bound from the other clause.