Shipowners are increasingly optimistic about a pickup in traffic through the Strait of Hormuz after more vessels left the waterway this week with the U.S. providing information to aid those making the journey. 

At least two shipowners, who asked not to be identified discussing sensitive information, said they were in touch with American military forces, which advised them on how best to navigate the waterway. A spokesperson for the U.S. Central Command said U.S. military assets aren’t escorting ships, but the command continues to provide advice to commercial vessels in the region.

One person with knowledge of a transit said a group of vessels was approached by suspected Iranian fast boats during the journey. The boats were turned away by helicopters that suddenly appeared nearby, allowing the person’s vessel to continue away from Hormuz, they said.

Chevron Corp. Chief Executive Officer Mike Wirth told Bloomberg TV on May 27 that some vessels transiting Hormuz have recently come under attack. On the same day, the U.S. affirmed that deals with Iran to safely sail through the Strait of Hormuz — even those which don’t involve paying a toll — are prohibited.

Some of the ships that have crossed belong to companies that hadn’t transited Hormuz since the war began, according to several people involved in shipping markets. Two people said some ships were entering the Persian Gulf as well as leaving. 

If sustained, the increase in transits could signal that more shipping companies are willing to make the journey, boosting the flow of everything from oil and gas to consumer goods. Until now, transits had largely been limited to vessels operating under bilateral government arrangements or owned by the small group of more-daring shipping executives willing to accept the risks of sailing through Hormuz. 

Regional countries, including the state oil company of the United Arab Emirates, have also sent ships through, while Qatar is quietly exporting liquefied natural gas to key buyers. 

Some of the vessels that crossed in recent days did so with their satellite transponders switched off, and have yet to turn them back on. It’s a sign that conventional vessel-tracking methods may understate how many vessels are making the voyage. 

Ship-tracking data show that at least a quarter of the non-Iranian ships stranded in Hormuz since the conflict began have made their way out.

The White House has repeatedly sent conflicting messages on the prospects for a deal with Iran, a pattern that continued on Friday. A fresh agreement between the two nations could potentially open the door for a broader reopening of shipping through Hormuz. 

Owners privately said they hope the agreement would allow for a resumption of Hormuz flows, but that uncertainty remained until its full details were known. Some said that until that agreement was reached, while it might be possible to get vessels out of Hormuz, many owners would remain reluctant to enter. 

TotalEnergies Chief Executive Officer Patrick Pouyanne said on May 27 that his company would want indications of lasting peace before sending vessels back into the Persian Gulf. 

A sustained resumption to shipping also has the potential to boost oil tanker earnings that are already the highest in a generation in the short-term, if a peace emerges that leaves shipowners comfortable to transit. 

“We would expect, if you like, a frenzy phase to start with,” once Hormuz reopens, Gerasimos Kalogiratos, Chief Executive Officer of Capital Tankers Corp., said on an earnings call in May. He added that tanker costs would stay high in the longer-term as global oil inventories refill barrels lost to the war.