We show that the dissociation threshold of an exciton, a bound electron-hole pair, by an electric field is mainly determined by its energy: as expected, the dissociation voltage decreases with increasing exciton energy. However, within the multiplet of states belonging to a particular principal quantum number n, the dissociation voltage rises with increasing state energy, in contrast to the expectations based on energy arguments. This behavior is demonstrated for the yellow exciton states of Cu₂O and is attributed to the distribution of the wavefunction in the potential landscape, where the lower (higher) lying state in the multiplet is shifted away (towards) the tunnel barrier.