The lack of annotated data is a big issue for building reliable NLP systems for most of the world's languages. But this problem can be alleviated by automatic data generation. In this paper, we present a new data augmentation method for artificially creating new dependency-annotated sentences. The main idea is to swap subtrees between annotated sentences while enforcing strong constraints on those trees to ensure maximal grammaticality of the new sentences. We also propose a method to perform low-resource experiments using resource-rich languages by mimicking low-resource languages by sampling sentences under a low-resource distribution. In a series of experiments, we show that our newly proposed data augmentation method outperforms previous proposals using the same basic inputs.