Oman wants an open Strait of Hormuz. Iran wants to keep control.
The two countries with shores on the vital waterway are at odds on the way forward.
With unresolved tensions over the strait prompting a 13-day exchange of strikes between the US and Iran this month, solving the puzzle is crucial to the Middle East and the world.
As attacks in the Red Sea increase the pressure on trade, new proposals have emerged this week from diplomats scrambling to find a solution.
What Oman wants
Omani Foreign Minister Badr Al Busaidi led a meeting of Gulf ministers on Tuesday. They discussed "ensuring the smooth flow of ships, trade and supplies" through the strait.
Details of what Oman has in mind were leaked through diplomats. The Omani proposal, reported by Reuters, calls for joint regional management of the waterway. It suggests voluntary fees to help fund the cost of navigation and services including search and rescue.
Tehran said it had also heard proposals from Muscat to design a route that is partly under Iranian control and partly under Omani control.
The Malacca model
The proposal for voluntary payments has been compared to arrangements for the Strait of Malacca, a trade route in South-East Asia.
The strait is managed by Indonesia, Malaysia and Singapore, with shipping companies paying into a voluntary fund for safe navigation. The fund does not make regular disclosures, but Singapore said in 2017 that $22 million had been raised over 10 years.
What Iran wants
Iran wants to maintain its grip on the strait, which it has used as a pressure tool during its war with the US and Israel. Tehran has also repeatedly raised the prospect of charging tolls on shipping, a proposal rejected by Gulf states and the US.
Deputy Foreign Minister Kazem Gharibabadi said on Tuesday that the strait "will never return to its pre-war state".
The two routes
There are two established routes through the strait. The northern one lies in Iranian waters, and Tehran has insisted on total control.
A southern route runs through Omani waters. Muscat has worked with the UN's International Maritime Organisation to make the route a "temporary maritime corridor" during the war.
But Iran opposes the use of that route, claiming it is "illegal and unsafe", and says it has attacked ships for attempting to sail along it. Mr Gharibabadi said Iran had rejected an Omani proposal for an equal division in the waterway.
He said Iran proposed that shipping traffic should pass through its waters in one direction and partly through its waters in the other direction. He said the strait would remain closed if Muscat rejected the Iranian proposal.
The IMO said it was not involved in the discussions. "Any proposal for new shipping routes or traffic management measures should be submitted to IMO for consideration by member states," a spokesman said. Tehran had never recognised the southern route along Oman's coast, he added.
