In this paper we present a normalization theorem for a natural deduction formulation of Zermelo set theory. Our result gets around M. Crabbe's counterexample to normalizability (Hallnäs [3]) by adding an inference rule of the form and requiring that this rule be used wherever it is applicable. Alternatively, we can regard the result as pertaining to a modified notion of normalization, in which an inference is never considered reducible if A is T Є T , even if R is an elimination rule and the major premise of R is the conclusion of an introduction rule. A third alternative is to regard (1) as a derived rule: using the general well-foundedness rule we can derive (1). If we regard (2) as neutral with respect to the normality of derivations (i.e., (2) counts as neither an introduction nor an elimination rule), then the resulting proofs are normal.