The exponential growth of DNA sequencing data limits the searchable proportion of the data. In this context, tokenization of genomic data via their k-merization provides a path towards efficient algorithms for their compression and search. However, indexing even single k-mer sets still remains a significant bioinformatics challenge, especially if k-mer sets are sketched or subsampled. Here, we develop the FMSI index, a space-efficient data structure for unconstrained k-mer sets, based on approximated shortest superstrings and the Masked Burrows Wheeler Transform (MBWT), an adaptation of the BWT for masked superstrings. We implement this in a program called FMSI, and via extensive evaluations using prokaryotic pan-genomes, we show FMSI substantially improves space efficiency compared to the state of the art, while maintaining a competitive query time. Overall, our work demonstrates that superstring indexing is a highly general, parameter-free approach for modern k-mer sets, without imposing any constraints on their structure.