Nowadays, Genomics has gained relevance since it allows preventing, diagnosing and treating diseases in a personalized way. The reduction in sequencing time and cost has increased the demand and, thus, the amount of genomic data that must be stored or transferred. Consequently, it becomes necessary to develop genome compression algorithms that help to reduce storage usage without consuming too much time. This is now possible thanks to modern multicore machines. This paper improves MtHRCM, a multi-threaded compression algorithm for large collections of genomes, by reducing its sequential component in order to enhance performance and scalability. Experimental results show that our optimized version is faster than MtHRCM and achieves the same compression ratio. Also, they reveal that this new version scales well when increasing the number of threads/cores for smaller test collections, while the high amount of simultaneous I/O requests to disk limits the scalability for larger test collections.