This article extends the subsequentialization algorithm of Mohri by generalizing it for previously untreated classes of transducers. A representational change allows for uniform representation, suitable for further calculus operations. An $epsilon$-closure set, and appropriate modifications using this set, make it possible to handle transducers containing input-side $epsilon$ labels. The closure is found directly, without any transformation of the original transducer. The <I>unknown symbol</I> which is an extension of the usual transducer notation, can be present, if handled specially, in sequentialization and in subsequent finite-state calculus operations and applications. The beneficial effects of these transformations have been tested in real natural language processing examples.

