We investigate the utility of right-context (look-ahead information) in incremental left-to-right lan-\linebreak guage models with word sense disambiguation, and discover somewhat unexpectedly that using right-context in addition to left-context (history) may actually \textit{reduce} accuracy. We employ word sense disambiguation as one component of a language model designed to allow hypothesis to be evaluated incrementally. In our baseline system, disambiguation is performed by a na\"{\i}ve-Bayes classifier that uses lexical co-occurrence features from the history. We then augment the left-context only model with three well-motivated methods using the right-context. Perhaps surprisingly, experiment results with the three look-ahead strategies shown a 0.19\% up to 10.04\% \textit{decrease} in the accuracy of disambiguating the next word.