Natural language processing for Greek and Latin, inflectional languages with small corpora, requires special techniques.For morphological tagging, transformer models show promising potential, but the best approach to use these models is unclear.For both languages, this paper examines the impact of using morphological lexica, training different model types (a single model with a combined feature tag, multiple models for separate features, and a multi-task model for all features), and adding linguistic constraints.We find that, although simply fine-tuning transformers to predict a monolithic tag may already yield decent results, each of these adaptations can further improve tagging accuracy.1 For example, for each type (unique word form) in the GUM English Universal Dependencies Treebank (see https://universaldependencies.org/) there are 10.7 tokens.For the Latin PROIEL treebank there are only 6.5, and for the Greek Perseus treebank even less, viz.4.8 (note that they are all roughly similar in size: 212K, 205K and 202K tokens respectively).