The Context-Free backbone of some natural language analyzers produces all possible CF parses as some kind of shared forest, from which a single tree is to be chosen by a disambiguation process that may be based on the finer features of the language. We study the structure of these forests with respect to optimality of sharing, and in relation with the parsing schema used to produce them. In addition to a theoretical and experimental framework for studying these issues, the main results presented are: sophistication in chart parsing schemata (. use of look-ahead) may reduce time and space efficiency.