We introduce Genozip Deep, a method for losslessly co-compressing FASTQ and BAM files. Benchmarking demonstrates improvements of 75% to 96% versus the already-compressed source files, translating to 2.3X to 6.8X better compression than current state-of-the-art algorithms that compress FASTQ and BAM separately. The Deep method is independent of the underlying FASTQ and BAM compressors, and here we present its implementation in Genozip, an established genomic data compression software.