With the advent of conversational assistants, like Amazon Alexa, Google Now, etc., dialogue systems are gaining a lot of traction, especially in industrial setting. These systems typically consist of Spoken Language understanding component which, in turn, consists of two tasks - Intent Classification (IC) and Slot Labeling (SL). Generally, these two tasks are modeled together jointly to achieve best performance. However, this joint modeling adds to model obfuscation. In this work, we first design framework for modularization of joint IC-SL task to enhance architecture transparency. Then, we explore a number of self- attention, convolutional, and recurrent models, contributing a large-scale analysis of modeling paradigms for IC+SL across two datasets. Finally, using this framework, we propose a class of ‘label-recurrent’ models that otherwise non- recurrent, with a 10-dimensional representation of the label history, and show that our proposed systems are easy to interpret, highly accurate (achieving over 30% error reduction in SL over the state-of-the-art on the Snips dataset), as well as fast, at 2x the inference and 2/3 to 1/2 the training time of comparable recurrent models, thus giving an edge in critical real-world systems.