On-line hand-drawn structured document interpretation is a complex problem of pattern recognition. This paper deals with eager strategies for such purpose, i.e. consisting in updating the analyzed document after each input stroke and providing a corresponding feedback to the user. We have designed a new class of visual grammars for the modeling of structured document composition: the context-driven constraint multiset grammars (CD-CMG). Their main originalities are to model the structural context in which a production can be reduced and to take into account the hand-drawn nature of the considered data. Its associated parser exploits the formalized knowledge for predictive purposes and couples bottom-up and top-down strategies. Their context-sensitiveness helps reducing significantly the combinatory associated to the analysis process. We use the fuzzy set framework to evaluate each possible interpretation on a qualitative way. Reject options are exploited to increase the decision making robustness and to detect the need for stroke segmentation. The parser is also able to wait for more information before making a decision by using a branch and bound algorithm. In this paper, we provide experimental results showing that the method is efficient enough to be used in real-time applications. We illustrate this point by focusing on a commercialized pen-based system that is based on the DALI method we present in this paper.