The Dravidian family is one of the most widely spoken set of languages in the world, yet there are very few annotated resources available to NLP researchers. To remedy this, we create DravMorph, a corpus annotated for morphological segmentation and part-of-speech. Also, we exploit novel features and higher-order models to achieve promising results on these corpora on both tasks, beating techniques proposed in the literature by as much as 4 points in segmentation F1.