The parsing component of previous principle-based machine translation systems are inefficient since they tend to adopt a generate-and-test paradigm. We combine the benefits of a message-passing paradigm with the benefits of a parametric approach in the implementation of a parser that avoids overgeneration and is easily ported to multiple languages. The algorithm has been implemented in C++ and successfully tested on well-known, translationally divergent sentences in a MT system called PRINCITRAN.