Conserved, ultraconserved and other classes of constrained elements (collectively referred as CNEs here), identified by comparative genomics in a wide variety of genomes, are non-randomly distributed across chromosomes. These elements are defined using various degrees of conservation between organisms and several thresholds of minimal length. We here investigate the chromosomal distribution of CNEs by studying the statistical properties of distances between consecutive CNEs. We find widespread power-law-like distributions, i.e. linearity in double logarithmic scale, in the inter-CNE distances, a feature which is connected with fractality and self-similarity. Given that CNEs are often found to be spatially associated with genes, especially with those that regulate developmental processes, we verify by appropriate gene masking that a power-law-like pattern emerges irrespectively of whether elements found close or inside genes are excluded or not. An evolutionary model is put forward for the understanding of these findings that includes segmental or whole genome duplication events and eliminations (loss) of most of the duplicated CNEs. Simulations reproduce the main features of the observed size distributions. Power-law-like patterns in the genomic distributions of CNEs are in accordance with current knowledge about their evolutionary history in several genomes.