We present labeled morphological segmentation—an alternative view of morphological processing that unifies several tasks. We introduce a new hierarchy of morphotactic tagsets and Chipmunk, a discriminative morphological segmentation system that, contrary to previous work, explicitly models morphotactics. We show improved performance on three tasks for all six languages: (i) morphological segmentation, (ii) stemming and (iii) morphological tag classification. For morphological segmentation our method shows absolute improvements of 2-6 points F1 over a strong baseline.