The Visual Multimethod Assessment Fusion (VMAF) algorithm has recently emerged as a state-of-the-art approach to video quality prediction, that now pervades the streaming and social media industry. However, since VMAF requires the evaluation of a heterogeneous set of quality models, it is computationally expensive. Given other advances in hardware-accelerated encoding, quality assessment is emerging as a significant bottleneck in video compression pipelines. Towards alleviating this burden, we propose a novel Fusion of Unified Quality Evaluators (FUNQUE) framework, by enabling computation sharing and by using a transform that is sensitive to visual perception to boost accuracy. Further, we expand the FUNQUE framework to define a collection of improved low-complexity fused-feature models that advance the state-of-the-art of video quality performance with respect to both accuracy, by 4.2% to 5.3%, and computational efficiency, by factors of 3.8 to 11 times!.