Most on-line cursive handwriting recognition systems use a lexical constraint to help improve the recognition performance. Traditionally, the vocabulary lexicon is stored in a trie (automaton whose underlying graph is a tree). In a previous paper, we showed that non-deterministic automata were computationally more efficient than tries. In this paper, we propose a new method for constructing incrementally small non-deterministic automata from lexicons. We present experimental results demonstrating a significant reduction in the number of labels in the automata. This reduction yields a proportional speed-up in HMM based lexically constrained pattern recognition systems.