The DNA double helix undergoes an ‘overstretching’ transition in a narrow force range near 65 pN. Despite numerous studies the basic question of whether the strands are separated or not remains controversial. Here we show that overstretching in fact involves two distinct types of double-helix reorganization: slow hysteretic ‘unpeeling’ of one strand off the other; and a fast, non-hysteretic transition to an elongated double-stranded form. We demonstrate that the relative fraction of these two overstretched forms is sensitive to factors that affect DNA base pair stability, including DNA sequence, salt concentration and temperature. The balance between the two forms shifts near physiological solution conditions. This result, in addition to establishing the existence of an overstretched double-stranded state, also shows that double helix physical properties are tuned so that either unpeeling or overextension can be selected via small changes in molecule environment