A key observation is that a degree-D Attardi system does not contain all possible transitions of degree within D. Since prior empirical work has ascertained that transition systems using more transitions with degree greater than 1 can handle more non-projective treebank trees <cite>(Attardi, 2006</cite>; Gómez-Rodríguez, 2016) , we hypothesize that adding some of these "missing" reduce transitions into the system's inventory should increase coverage.