Recently, several authors have argued that Gricean theories of scalar implicature computation are inadequate, and, as an alternative, one author has proposed a grammatical system for computing scalar implicatures. The present paper provides arguments, counter to the'claims of these authors, that Gricean reasoning can account for the implicatures of certain complex sentences and does not generate undesirable implicatures for others. Moreover, it is shown that a putative advantage of grammatical scalar implicature computation, that it informs a theory of intervention in negative polarity item licensing, is spurious. These arguments, plus general conceptual advantages of Gricean theory, lead to the conclusion that scalar implicature computation is not carried out in the grammar.