RNA-sequencing (RNA-seq) is increasingly used to diagnose patients with rare diseases by prioritising genes with aberrant expression and/or splicing. State-of-the-art methods for detecting aberrant expression and splicing, however, are extremely slow. The latter, also discard much information because they only use junction reads to infer aberrant splicing. In this contribution, we show that replacing the offset for library size unlocks conventional bulk RNA-seq workflows for fast and scalable differential usage, aberrant splicing and expression analyses. Our method, saseR, is several orders of magnitude faster than the state-of-the-art methods and dramatically outperforms these in terms of sensitivity and specificity for aberrant splicing, while being on par with these inferring differential usage and aberrant expression. Finally, our framework is also very flexible and can be used for all applications that involve the analysis of proportions of short- or long RNA-seq read counts.