For a few years, it has been possible to experimentally probe the universe of cis and trans RNA–RNA interactions in a transcriptome-wide manner. These experiments give rise to so-called duplex data, i.e. short reads generated via high-throughput sequencing that each encode information on a cis or trans RNA–RNA interaction. These raw duplex data require complex, subsequent computational analyses in order to be interpreted as solid evidence for actual cis and trans RNA–RNA interactions. While several methods have already been proposed to tackle this challenge, almost all of them lack one or more desirable feature—computational efficiency, ability to readily alter the main processing steps and parameter values, p-value estimation for predictions, and interoperability with the common bioinformatics tools for transcriptomics. To overcome these challenges, we present DuplexDiscoverer—a computational method and R package that allows for the efficient, adjustable, and conceptually coherent analysis of duplex data. DuplexDiscoverer is readily adaptable to analysing data from different experimental protocols and its results seamlessly integrate with the most commonly used bioinformatics tools for transcriptomics in R. Most importantly, DuplexDiscoverer generates predictions that are of superior or comparable quality to those of the existing methods while significantly improving time and memory efficiency.