MAE_ToBI, the gold-standard of intonation annotation for American English, aims to provide an annotation system of the categorical (phonemic) aspects of intonation. In this way, a single MAE_ToBI label is used for multiple f0 contours; thus, by design, many aspects of the prosody are not transcribed. If the ToBI labels are a primary source for linguistic analysis, an important concern should be: without this untranscribed information, can our models of intonation be complete? In this talk, I will discuss a few of my ongoing collaborative research projects that aim to address this question, and I will also workshop an (English-specific) annotation system which captures more phonetic variation, and which is still under development. This type of work is highly relevant for intonational phonology (as well as for theoretical models that interact with intonation): until various types of intonational phonetic variation are better documented, models of intonational phonology will remain incomplete.