In previous work, we showed that using a lattice instead of the 1-best path to represent both the query and the utterance being searched is beneficial for spoken keyword spotting. In this paper, we introduce several techniques that further improve our multi-lattice alignment approach, including edit operation modeling and supervised training of the conditional probability table, something which cannot be directly trained by traditional maximum likelihood estimation. Experiments on TIMIT show that the proposed methods significantly improve the performance of spoken keyword spotting.