There are two orthogonal methodologies for efficient prediction of data races from concurrent program runs: commutativity and prefix reasoning. There are several instances of each methodology in the literature, with the goal of predicting data races using a streaming algorithm where the required memory does not grow proportional to the length of the observed run, but these instances were mostly created in an ad hoc manner, without much attention to their unifying underlying principles. In this paper, we identify and formalize these principles for each category with the ultimate goal of paving the way for combining them into a new algorithm which shares their efficiency characteristics but offers strictly more prediction power. In particular, we formalize three distinct classes of races predictable using commutativity reasoning, and compare them. We identify three different styles of prefix reasoning, and prove that they predict the same class of races, which provably contains all races predictable by any commutativity reasoning technique. Our key contribution is combining prefix reasoning and commutativity reasoning in a modular way to introduce a new class of races, granular prefix races, that are predictable in constant-space and linear time, in a streaming fashion. This class of races includes all races predictable using commutativity and prefix reasoning techniques. We present an improved constant-space algorithm for prefix reasoning alone based on the idea of antichains (from language theory). This improved algorithm is the stepping stone that is required to devise an efficient algorithm for prediction of granular prefix races. We present experimental results to demonstrate the expressive power and performance of our new algorithm.