Abstract. This paper extends the recent work [CMT00] on the operational semantics and type system for a core language, called MiniMLBN ref , which exploits the notion of closed type (see also [MTBS99]) to safely combine imperative and multi-stage programming. The main novelties are the identification of a larger set of closed types and the addition of a binder for useless variables. The resulting language is a conservative extension of MiniMLref , a simple imperative subset of SML.