Dependency grammar has a long tradition in syntactic theory, dating back to at least Tesni~re's work from the thirties3 Recently, it has gained renewed attention as empirical methods in parsing are discovering the importance of relations between words (see, ., (Collins, 1997)), which is what dependency grammars model explicitly do, but context-free phrasestructure grammars do not. One problem that has posed an impediment to more wide-spread acceptance of dependency grammars is the fact that there is no computationally tractable version of dependency grammar which is not restricted to projective analyses. .