Failure to maintain organelle genome stability has been linked to numerous phenotypes, including variegation and cytosolic male sterility (CMS) in plants, as well as cancer and neurodegenerative diseases in mammals. Here we describe a next-generation sequencing approach that precisely maps and characterizes organelle DNA rearrangements in a single genome-wide experiment. In addition to displaying global portraits of genomic instability, it surprisingly unveiled an abundance of short-range rearrangements in Arabidopsis thaliana and human organelles. Among these, short-range U-turn-like inversions reach 25% of total rearrangements in wild-type Arabidopsis plastids and 60% in human mitochondria. Furthermore, we show that replication stress correlates with the accumulation of this type of rearrangement, suggesting that U-turn-like rearrangements could be the outcome of a replication-dependent mechanism. We also show that U-turn-like rearrangements are mostly generated using microhomologies and are repressed in plastids by Whirly proteins WHY1 and WHY3. A synergistic interaction is also observed between the genes for the plastid DNA recombinase RECA1 and those encoding plastid Whirly proteins, and the triple mutant why1why3reca1 accumulates almost 60 times the WT levels of U-turn-like rearrangements. We thus propose that the process leading to U-turn-like rearrangements may constitute a RecA-independent mechanism to restart stalled forks. Our results reveal that short-range rearrangements, and especially U-turn-like rearrangements, are a major factor of genomic instability in organelles, and this raises the question of whether they could have been underestimated in diseases associated with mitochondrial dysfunction.