This paper presents a new approach to two challenging NLP tasks in Classical Tibetan: word segmentation and Part-of-Speech (POS) tagging. We demonstrate how both these problems can be approached in the same way, by generating a memory-based tagger that assigns 1) segmentation tags and 2) POS tags to a test corpus consisting of unsegmented lines of Tibetan characters. We propose a three-stage workflow and evaluate the results of both the segmenting and the POS tagging tasks. We argue that the Memory-Based Tagger (MBT) and the proposed workflow not only provide an adequate solution to these NLP challenges, they are also highly efficient tools for building larger annotated corpora of Tibetan.