This communication sets the problem of incremental parsing in the context of a complete incremental compiling system. It turns out that, according to the incrementally paradigm of the attribute evaluator and data-flow analyzer to be used, two definitions of optimal incrementality in a parser are possible. Algorithms for achieving both forms of optimality are given, both of them based on ordinary LALR(1) parse tables. Optimality and correctness proofs, which are merely outlined in this communication, are made intuitive thanks to the concept of awell-formed list of threaded trees, a natural extension of the concept ofthreaded treefound in earlier works on incremental parsing.