This study extends LaFrance's (1985, 1986, 1990) previous research by deriving the necessary parameter restrictions for two additional classes of incomplete demand system models to be integrable. In contrast to LaFrance's earlier work, this analysis considers models that treat expenditures and expenditure shares as the dependent variables in the specified incomplete demand systems. With environmental economists increasingly turning to demand system approaches to value changes in environmental quality, these new results significantly expand the menu of empirical specifications which can be used to fit a given data set. Moreover, the alternative specifications considered in this study, in combination with LaFrance's original work, represent a complete characterization of the linear, log-linear, and semi-log incomplete demand system models.