An article from September 10 in The Globe and Mail discussed the possibility of Canada and Denmark working out a solution to the conflict over Hans Island. The half-square mile island has technically been in dispute since 1973. A treaty was signed between the two Arctic nations regarding the delimitation of the Canadian and Greenlandic continental shelves, but one small portion of the region within the Nares Strait was left undelimited. Hans Island falls within that area.
The article quotes Professor Michael Byers of the University of British Columbia as saying that there are no known resources under the island, which should make the dispute easier to resolve. However, according to author Rongxing Guo, there are three other factors which may make the territorial issue somewhat thornier.
Firstly, Hans Island is located in the center of the Kennedy Channel in the Nares Strait, which is important for navigation, as it flows between Ellesmere Island and Greenland. While the Nares Strait is usually frozen, in August, the low amount of ice makes it navigable. But this type of condition could become more permanent once the ice further melts, making the passage a more practical route for transportation and shipping. On the contrary, the route is very far north, which could work against turning the Nares Strait into a popular shipping channel. Secondly, winning control of Hans Island could give either Canada or Denmark a strong precedent for other Arctic claims. Sovereignty and national pride are at stake here, with both countries having set foot on the island and planting flags. Finally, the channel is a prime spot for oil companies to test how their artificial islands and platforms for oil rigs, would stand up to ice floes. 
Two possible solutions he suggested are that
“Canada and Denmark could consider dividing the island in half, with each getting a side, or [create] a so-called condominium of shared sovereignty. Each country … could take turns during the year administering it.”
Byers cited the example of Pheasant Island, which France and Spain jointly control. The island, which lies in the center of the River Bidasoa running along the border between the two countries, is controlled by France for six months out of the year and then by Spain during the other half of the year.
There have been no formal discussions about the territoriality of Hans Island since May 2008, though a spokesperson from Canada’s Ministry of Foreign Affairs remarked that “negotiations are on a diplomatic track.” There is no deadline for a resolution, but if none is ever reached, both Canada and Denmark have agreed to take the issue to the International Court of Justice.
 Territorial Disputes and Resource Management: A Global Handbook, by Rongxing Guo.
Professor Byer runs an informative blog on the Arctic.