Complex chromosomal rearrangements consist of structural genomic alterations involving multiple instances of deletions, duplications, inversions, or translocations that co-occur either on the same chromosome or represent different overlapping events on homologous chromosomes. We present SVelter, an algorithm that first identifies regions of the genome suspected to harbor a complex event and then iteratively rearranges the local genome structure, in a randomized fashion, with each structure scored against characteristics of the observed sequencing data. We show that SVelter is able to accurately reconstruct these regions when compared to well-characterized genomes that have been deep sequenced with both short and long read technologies.