Full-reference and reduced-reference image quality assessment (IQA) models assume a high quality reference against which to measure perceptual quality. However, this assumption may be violated when the source image is upscaled, poorly exposed, or otherwise distorted before being compressed. Reference IQA models on a compressed but previously distorted “reference” may produce unpredictable results. Hence we propose 2stepQA, which integrates no-reference (NR) and reference (R) measurements into the quality prediction process. The NR module accounts for imperfect quality of the reference image, while the R component measures further quality from compression. A simple, efficient multiplication step fuses these into a single score. We deploy MS-SSIM as the R component and NIQE as the NR component and combine them using multiplication. We chose MS-SSIM, since it is efficient and correlates well with subjective scores. Likewise, NIQE is simple, efficient, and generic, and does not require training on subjective data. The 2stepQA approach can be generalized by combining other R and NR models. We also built a new data resource: LIVE Wild Compressed Picture Database, where authentically distorted reference images were JPEG compressed at four levels. 2stepQA is shown to achieve standout performance compared to other IQA models. The proposed approach is made publicly available at https://github.com/xiangxuyu/2stepQA.