Like much of this coast, the island wears a layer of imported names over its older one. Matthew Flinders, charting Australia in 1803, called it Melville Island, after one of his patrons. The trouble was that a far larger Melville Island lay north of Darwin, in Tiwi country, and the duplication caused enough confusion that in 1934 the island was renamed Bremer, after Sir James Gordon Bremer, who had founded the short-lived European outpost of Fort Dundas on that other Melville Island in 1824. Fort Dundas failed and was abandoned by 1828. Through all of it, the island kept the name its traditional owners had always used: Dhambaliya. The European labels record who passed by; the Yolngu name records who belongs.

Tourism here is deliberately tiny. The island's only visitor facility is the Banubanu Beach Retreat at its northern tip, established in the early 2000s on Yolngu-owned freehold land under an agreement with the traditional owners. The rules keep the footprint small: no more than twelve guests stay at any one time, and alcohol is effectively banned, permitted only in small quantities for those visitors. The result is a rare kind of remoteness, reached by a short charter flight from Gove or an hour on the water, where the loudest sounds are wind, surf and seabirds. The retreat doubles as a private wildlife sanctuary, and the limit on numbers is not a marketing gimmick but a way of protecting the nesting turtles and the birds that share the sand.

Dhambaliya is ringed almost entirely by beach, and that beach is the point. The turtles that nest here are part of a wider web of life along this stretch of the Gulf of Carpentaria, and the island is home to many bird species besides. A few kilometres east lie the East Bremer Islets, a scatter of small rocky outcrops including Higginson Island, important enough to migratory and breeding seabirds to be recognised as the Higginson Important Bird Area. A family outstation in the island's north, near the airstrip, anchors the human presence: a couple of dozen Rirratjingu people living on country, keeping the connection unbroken. The island is small and lightly inhabited, but it is not empty, and it is certainly not wild in the sense of being unowned.

From the northern beaches you can see the mainland of Arnhem Land, the town of Nhulunbuy only a short hop away, its refinery and harbour part of a different century's idea of value. Dhambaliya offers the older idea: a place measured not in tonnes extracted but in turtles returning, seasons turning, and knowledge passed down. To come here is to slow to the island's pace, governed by tide and weather and the careful permissions of its owners. The Arafura Sea has carried Macassan fishermen, British charts and modern travellers past this shore, but the island has stayed, quietly, Rirratjingu country, doing what it has always done.