In logic, quantifiers typically have an implicit linear order of dependencies. Henkin introduced a more general framework for quantifier prefixes, allowing for partial orderings among quantifiers. These quantifiers, now known as Henkin quantifiers, have been extensively studied in logic and have found significant applications in linguistics, arithmetic, and descriptive complexity. Surprisingly, bounded versions of Henkin quantifiers, which restrict the range of these quantifiers, have not been explored. This paper defines bounded Henkin quantifiers and examines their properties from a complexity-theoretic perspective. In particular, we show that the set of predicates definable by quantifier-free formulas prefixed by a bounded Henkin quantifier is exactly \(\textsf{NEXPTIME}\) . The proof goes via machine models defined using bounded Henkin quantifiers. Finally, we show that formulas with Henkin quantifiers define a complexity class contained in \(\varDelta _2\) in the exponential hierarchy and define a natural complete problem for this class.