Arbitrary amplitude dust-acoustic double-layers (DA-DLs) in two high-energy tail ion distributions are investigated. The electron number density has been assumed sufficiently depleted during the charging of dust grains on account of the attachment of background plasma electrons on the surface of dust grains. It is found that under certain conditions DA-DLs may be admitted. The degree of suprathermality of the low-temperature component has a sensitive role on their formation and a small change in this degree can even prevent the DL formation. The ‘Maxwellianization’ of the high-temperature component involves a suprathermalization process of the low-temperature component for the existence of localized DA-DLs. Our results may be relevant to a number of space dusty plasma systems, particularly the Saturn's F-ring where electron depletion and suprathermality are thought to come into play.