In this dissertation, I show that due to the unique hierarchical properties of syntactic features, innovation can reveal inherited structural relationships that would otherwise remain opaque. Based on this idea, I propose a disharmonically headed reconstruction of Proto-Indo-European (PIE) clausal syntax; specifically, I argue that PIE was left-headed in the CP domain and right-headed in the TP domain, and provide additional evidence that PIE was right-headed within VP as well. The novelty of my approach compared to those of my predecessors is looking at the various auxiliary constructions innovated across the Indo-European (IE) daughter languages instead of focusing exclusively on reconstructible lexical verbs. This approach allows me to more accurately triangulate the location of inflection in the syntax relative to the lower verbal domain, which gives me more accurate information about the featural makeup of the functional heads of these languages and improves my resulting reconstruction. To strengthen my conclusions, I provide extensive auxiliary data from corpora of six of the earliest attested Indo-European languages: Hittite, Tocharian, Vedic Sanskrit, Homeric Greek, Old Latin, and Gothic. For each language, I categorize all word order variations seen in the auxiliary constructions, demonstrate that clauses ending with a verbal element (usually a participle) followed immediately by the auxiliary is by far the most common order attested, and show that in each of these languages these facts are most readily explained with a left-headed CP, right-headed TP analysis. I then provide all examples of auxiliary constructions from my corpora showing any other word order, and demonstrate that this word order variation is most straightforwardly derivable from an underlying right-headed TP structure. This project illustrates just how valuable and robust feature-based syntactic reconstruction can be. As Kim (2018) states, it is currently assumed that the innovations useful for subgrouping "may be phonological, morphological, or lexical". This project and others like it can help show the value of syntactic isoglosses for subgrouping purposes as well, and can even take the original idea a step further, showing that in some cases we can reconstruct syntactic information where we cannot reconstruct corresponding phonological or morphological information. This means that not only can we now subgroup based on inherited syntactic constructions, but also based on the syntactic features gleaned from constructions independently innovated in the daughter languages.