Motivation: High-coverage sequencing data have significant, yet hard to exploit, redundancy. Most FASTQ compressors cannot efficiently compress the DNA stream of large datasets, since the redundancy between overlapping reads cannot be easily captured in the (relatively small) main memory. More interesting solutions for this problem are disk-based~(Yanovsky, 2011; Cox et al., 2012), where the better of these two, from Cox~{\it et al.}~(2012), is based on the Burrows--Wheeler transform (BWT) and achieves 0.518 bits per base for a 134.0 Gb human genome sequencing collection with almost 45-fold coverage. Results: We propose ORCOM (Overlapping Reads COmpression with Minimizers), a compression algorithm dedicated to sequencing reads (DNA only). Our method makes use of a conceptually simple and easily parallelizable idea of minimizers, to obtain 0.317 bits per base as the compression ratio, allowing to fit the 134.0 Gb dataset into only 5.31 GB of space. Availability: http://sun.aei.polsl.pl/orcom under a free license.