This paper investigates new design options for the feature space of a dependency parser. We focus on one of the simplest and most efficient architectures, based on a deterministic shift-reduce algorithm, trained with the perceptron. By adopting second-order feature maps, the primal form of the perceptron produces models with comparable accuracy to more complex architectures, with no need for approximations. Further gains in accuracy are obtained by designing features for parsing extracted from semantic annotations generated by a tagger. We provide experimental evaluations on the Penn Treebank.