This paper summarizes recent work at Microsoft on the development of novel direct models. The key characteristic of our approaches is the use of long-span segment level features that relate acoustic properties directly to words. In this approach, the frame-level Markov assumption is replaced by the segment level Markov property, allowing us to extract long-span features. A key issue we address is the definition of generalizable features which allow us to model unseen words. We review two recently developed models that have this property: Flat Direct Models (FDMs), and Segmental CRFs (SCRFs). The first operates in a log-linear framework, and uses utterance level features. The second is also a log-linear model, but defines features at the word-segment level. We present new experimental results comparing the two approaches. We find that both show consistent improvements over a baseline system, and that the extra context available to the FDM enables slightly better performance in a re...